Earlier this month, for the first time ever, the BBC made every episode of 'Nu Who' – from 2005's Rose to the 2017 Christmas special, Twice Upon a Time – available to watch on iPlayer. In anticipation of Jodie Whittaker's debut series, fans can now catch up on all ten series of 21st-century Doctor Who to date, along with every special. As the Eleventh Doctor put it: "So come on, then. Take it! Take it all, baby! Have it! You have it all!"

But do you remember them all? The one with the giant crabs?* Or that time the Eleventh Doctor houseshared?** Or when the Twelfth Doctor ended up on Tumblr?*** No? Here are ten criminally underrated episodes – 'hidden gems', one from each series – that you definitely shouldn't skip…

The End of the World (2005)

"Earth death is scheduled for 15:39, followed by drinks in the Manchester Suite…"

Christopher Eccleston's sole series as the Ninth Doctor transformed Doctor Who from 'that old show your dad used to watch' into one of the BBC's freshest, funnest, biggest hits. Opener Rose introduces us to the Tylers – Billie Piper's Rose and her mum, Jackie, and boyfriend, Mickey – and subsequent instalments give us Slitheen in Downing Street, Daleks, Reapers, "Are you my mummy?" and Captain Jack. But don't overlook The End of the World (Series 1: 2). It's Rose Tyler's first trip off-world – to a space station in the year five billion, where the great and the not-so-good have gathered to watch the Earth burn, to the strains of Britney Spears' Toxic. Fall head over heels for the Face of Boe, the Moxx of Balhoon, Lady Cassandra ("Moisturise me!") and the Adherents of the Repeated Meme. See the Doctor flirting – with a tree. See the tree flirting back! It's utterly, mesmerisingly bonkers.

School Reunion (2006)

By 2006, we had a new Doctor, played by David Tennant. He and Rose meet Cybermen, Ood, half-alien cat-like nuns, the Abzorbaloff and the Devil himself. Episodes like Tooth and Claw, The Girl in the Fireplace and the series finale, Army of Ghosts/Doomsday – topped off with a Christmas special, The Runaway Bride, that introduces Catherine Tate as companion-to-be Donna Noble – cemented Nu Who's place in the national consciousness. So why doesn't School Reunion (Series 2: 3) make more fans' Top Ten lists? This must contravene several galactic laws?!

Because School Reunion is magical. Actual, 21st-century TV magic. It's the episode that brings back Elisabeth Sladen as Sarah Jane Smith, companion to the Third and Fourth Doctors. "After all those years, Sarah Jane lived again, and breathed again, and was, if anything, bigger than she had been back in the day," recalled Tennant, in 2011. "Even if you didn't know who Sarah Jane was, we were telling a story about Rose and how she deals with that… But then, of course, you want to tell that story of Sarah Jane – and that magic comes back…There was something magical about Lis."

In time, Sladen would get her own spin-off show, The Sarah Jane Adventures. Also, she'd return to Doctor Who for the 2008 series finale and, fleetingly, Tennant's swan-song in 2010. But School Reunion is where her comeback began. And it's a beautiful thing to see.

Gridlock (2007)

The 2007 series introduced us to Martha Jones, the Weeping Angels and Wilfred Mott, paired the Doctor with Shakespeare, turned the Time Lord human, and resurrected the Master not once, but twice – in the forms of Sir Derek Jacobi and John Simm. In fact, 2007 may be the show's starriest year yet. Other guest actors include future Academy Award nominees Andrew Garfield and Carey Mulligan, as well as pint-sized popstress Kylie Minogue. But don't get starstruck and miss out on Gridlock (Series 3: 3), scripted by showrunner Russell T Davies. It's a story set in the far, far future, on an underground motorway – inspired by Mega City One from 2000 AD's Judge Dredd comics – 50,000 light-years from Earth. And it's one of Doctor Who's most uplifting tales.

Come for the giant, gas-guzzling crabs – the Macra, appearing in Doctor Who for the first time in 40 years. Stay for the satire of mankind's faith in the benevolence of government, and a tearjerking rendition of Abide with Me. "We could have had a motorway full of rage, and pirates, and chainsaws," explained Davies, in 2007, "but I wanted to show a world that had adapted to its circumstances, with faith and hope. A very human thing to do."

Partners in Crime (2008)

"You're not mating with me, sunshine!"

2008 Doctor Who is the TV show at its most self-assured. It positively swaggers – from 1st-century Pompeii, to the Ood's ice-covered home world, to the crystalline planet Midnight. The Doctor gains a daughter, Alex Kingston's River Song arrives, planets go missing and so does Agatha Christie! Old monsters return for the first time since the 80s – hello to the Sontarans and Davros ("Behold! The apotheosis of my genius!"). With so much going on, you might forget to savour the series opener, Partners in Crime (Series 4: 1). But don't. It's good. Really good. Not as good as Midnight. Nothing's as good as Midnight. But that's not Partners in Crime's fault.

The Doctor and Donna's reunion, around 22 minutes in, is one of the show's funniest-ever scenes. The Adipose are as adorable as they are grotesque. That shock cameo at the end will send shivers down your spine. Most of all, though, this episode belongs to Catherine Tate, back as Donna for this 2008 series after her 'one-off' appearance in the 2006 Christmas special. Truth is, the Doctor just wants a mate. In Donna Noble, he found one of his best.

The Lodger (2010)

As 2010 dawned, Tennant's Doctor departed, Matt Smith's arrived ("Geronimo!"), and Steven Moffat took over as showrunner. His first series contains some of the show's all-time greatest hits: like The Eleventh Hour (which introduces not only Smith, but also Karen Gillan and Arthur Darvill as soon-to-be husband and wife Amy and Rory), the Richard Curtis-penned Vincent and the Doctor (a compassionate view of mental illness, told through the story of van Gogh's final weeks), and two-parter The Pandorica Opens/The Big Bang (as epic a series finale as Nu Who's ever seen).

However, sandwiched between those encounters with van Gogh and the Pandorica sits The Lodger (Series 5: 11), a gentler, less-assuming episode, written by Gareth Roberts. Based on Roberts' 2006 Doctor Who Magazine comic strip of the same name, The Lodger sees the Doctor move in with James Corden's Craig. They argue, mainly. Then go for a kick-about in the park. And solve mysteries together. And rescue Amy. Surprisingly, it's glorious. In fact: "It's art," insists the Doctor. "A statement on modern society. Ooh, ain't modern society awful." Matt Smith is great, obviously. The Eleventh Doctor has rarely been written better. And love saves the day. What's not to like?

The Girl Who Waited (2011)

A sensational two-parter, The Impossible Astronaut/Day of the Moon, launches the 2011 series as it means to go on: at breakneck speed – a thrilling onslaught of times, places and ambitious ideas. A pirate-studded prequel to a forgotten 1966 Hartnell historical? Bring it on! The Doctor's TARDIS becomes a living, breathing, human woman ("I think you call me Sexy")? Let's do it! A mid-season finale that introduces the 'Paternoster Gang' (Vastra, Jenny and Strax), reveals the identity of River and ends with the caption: 'THE DOCTOR WILL BE BACK IN LET'S KILL HITLER'? Hey, why not! From Amy's pregnancy, to the Cyber invasion of Colchester, to punching the Führer and locking him in a cupboard (Rory: "Shut up, Hitler!"), the 2011 series is the most fun you can have with your clothes/Silence-adapted, self-repairing, NASA spacesuit on.

Amongst all the crazy, The Girl Who Waited (Series 6: 10) offers a respite. Essentially, it's a three-hander between Amy, Rory and the Doctor set on the quarantined planet Apalapucia. And it's underrated. A highpoint of Nu Who. Karen Gillan's portrayal of 'old Amy', who's been separated from the Doctor and Rory for 36 years, is flawless. "It's not about what I'm doing, but who I'm doing it for." This one will move you to tears.

Dinosaurs on a Spaceship (2012)

Series 7, which spanned 2012 and 2013, had movie-sized aspirations. Each week a blockbuster – from the ruins of Skaro, to the Wild West, to 1930s New York, and a journey to the centre of the TARDIS. Old adversaries resurfaced – the Great Intelligence from the Troughton era, the Zygons from Tom Baker's second season. Amy and Rory departed. Clara Oswald arrived – three times. John Hurt debuted as the War Doctor. As did Peter Capaldi's Twelfth Doctor, in 50th anniversary special The Day of the Doctor – ahead of his first full series, in 2014. Before that, though, we had Dinosaurs on a Spaceship (Series 7 Part 1: 2) – what a title! – and there aren't many Saturday-teatime TV dramas that could pull this off…

It's written by Chris Chibnall, Doctor Who's new showrunner for 2018, and gives the Eleventh Doctor a gang ("Not really had a gang before. It's new") – alongside Amy and Rory there's Egyptian queen Nefertiti, big-game hunter Riddell, and Brian Williams, Rory’s dad. Also, David Mitchell and Robert Webb guest star as a pair of bickering robots. Prior to his role as the First Doctor in the 2017 Christmas special, David Bradley plays the despicable Solomon. It's big, loud and fun. And did we mention dinosaurs? On a spaceship!

Kill the Moon (2014)

The moon is an egg. Get over it.

Okay, but also Kill the Moon (Series 8: 7) – in which the Doctor, Clara and Coal Hill student Courtney crash-land on the lunar surface, to find a base full of corpses, vicious spider-like creatures and a terrible dilemma – is one of the Capaldi era's most captivating adventures. Other 2014 episodes – such as Listen, Mummy on the Orient Express, Flatline and two-part finale Dark Water/Death in Heaven – may get more attention, as does Michelle Gomez's show-stopping arrival as Missy… Also, this was Peter Capaldi's first series. He and Jenna Coleman's Clara travel inside a Dalek, meet Robin Hood, and rob a bank. And Earth is invaded by trees, then by Cybermen. Sure, that stuff grabs the headlines. But Kill the Moon? Now, that's smart and thought-provoking telly. And only the genius of Doctor Who could have birthed it.

Also, the moon is an egg.

Sleep No More (2015)

"You must not watch this. I'm warning you. You can never un-see it."

In 2015, the Doctor hung with Davros on Skaro for the first time since 1979's Destiny of the Daleks, met the immortal Me (née Ashildr), lost Clara, found Gallifrey, met Matt Lucas' Nardole, and spent billions of years in a confession dial. Also, he made the anti-war speech to end all speeches ("I'm unforgivable. Well, here's the unforeseeable: I forgive you"). But it would be a tragedy of Shakespearean proportions to snooze through Sleep No More (Series 9: 9), a genuinely terrifying, base-under-siege drama – and capitalist satire – written by Who stalwart Mark Gatiss. It's set on a space station in the 38th century, in a future where sleep is becoming obsolete. Uniquely, the episode is told entirely through 'found footage' – CCTV, surveillance cameras, helmet-camera-style POV shots. And it's a doozy.

"Really," said Gatiss, in 2015, "what humanity is doing is bartering away the most blessed thing there is: sleeping. Shakespeare and all the poets were right. There's more to it than we know. It's not just about having 40 winks; it's empirically right for us to do – otherwise the monsters will get us!"

Knock Knock (2017)

The 2017 series introduced the world to Bill Potts, played by Pearl Mackie. Before long, she ended up saving it. With lots else to enjoy too – the return of the Ice Warriors, the Cybermen and the Master, the redemption of Missy, the so-called 'Monk trilogy', one last hurrah for the First and Twelfth Doctors – you'd think you'd be forgiven for forgetting 'hidden gem' Knock Knock (Series 10: 4). You'd be wrong. The 'Dryads' don't forgive. Those alien insects will swarm over your body, break you down at a cellular level and turn you into wood, like they did to poor Eliza in Knock Knock. Hear that ominous, spine-tingling creaking sound behind you? That's them.

You should be bursting, teeming, swarming to watch straight-up horror story Knock Knock. David Suchet guest stars as the sinister Landlord. Writer Mike Bartlett is a huge fan of the Seventh-Doctor-and-Ace era, and it shows. (The episode echoes 1989 'haunted house' story Ghost Light, and we're barely two minutes into Knock Knock before a character has dropped a 'Wicked!') Also, Little Mix is on the soundtrack. Bill Potts proves herself, once again, to be the perfect companion to the Twelfth Doctor. And once you've binge-watched these ten 'hidden gems' – and the other 135 episodes of 'Nu Who' available on BBC iPlayer, too – you might well want to heed the Twelfth Doctor's advice to Eliza: "What's the point of surviving if you never see anyone; if you hide yourself away from the world? When did you last open the shutters?"

What we're saying is, go out and get some fresh air.

 

*The Macra, in Gridlock
**With Craig, in The Lodger
***Courtney's Tumblr, in Kill the Moon