I haven't laughed so much at a film that wanted me to laugh at it in years.

The year is 2018, and there are Nazis on the moon.

In the last days of the Second World War, a secret Nazi space programme fled to the dark side of the moon. For seventy years, they have hoarded their resources in secret, building a space armada, for one day, the Fourth Reich—the Moon Reich—intends to return to Earth in triumph.

When astronaut James Washington (Christopher Kirby) is sent to the moon as part of a campaign stunt—the first manned moon landing in fifty years!—to boost the re-election prospects of the President of the United States (a President who, by the way, bears no small resemblance to a certain former Governor of Alaska), his unlucky co-pilot sets the Lunar Lander down a bit too close to the Nazi Moonbase. When he's captured by the moon Nazis, the Moon Führer (Udo Kier) decides he must be a scout for an imminent Earth invasion. The Fourth Reich must act now. All they need is a computer powerful enough to run their doomsday weapon, the Götterdämmerung . . . which they would have already, except for the fact that Washington's smartphone battery has just run out. Two Nazi officers, the ambitious Klaus Adler (Götz Otto) and the idealistic Earth specialist Renate Richter (Julia Dietze), his fiancée, travel to Earth in the company of an aryanised Washington to find more computers and prepare the way for the invasion. But Adler has plans that involve him becoming Führer, and they require getting close to the US President.

Meanwhile, the POTUS (Stephanie Paul) is having problems: it'll take a miracle to get re-elected. When her campaign manager and image consultant, Vivian Wagner (Peta Sergeant) presents her with the two Nazis, she's delighted. They go on to transform her campaign Nazi-style, with outward success, although neither Wagner, Richter, nor the President herself is aware of Adler's plans to destroy the United States and depose the current Moon Führer. When Richter discovers her peace, love and fluffy bunnies image of Nazism doesn't actually conform to historical reality, she joins forces with Washington to oppose Adler.

But by this time, Adler has become Führer, and the Nazi invasion is already underway. While Vivian Wagner commands the USS George W. Bush, a nuclear-armed space ship, against the Nazi space flotilla, and a meeting of international diplomats devolves into fisticuffs, Richter and Washington race against time to disable the Götterdämmerung and save the Earth.

Blackly comic, self-consciously retro, Iron Sky is six parts pulp science fiction to five parts political satire, with a leavening of madcap antics and humorous caricature. I find it hard to analyse it with sober and sensible thought: I spent too much time while I was watching it (twice) in mad, breathless giggles. Let me outline some elements that really worked for me:

The steampunk-esque (diesel-punk?) atmosphere of the Nazi moonbase. The Moon Reich's technological aesthetic has not changed since the 1940s. Brass dials and levers are operated by mad German scientists, and the design of Nazi spacesuit helmets is a variation on the gas mask. It is very much a retro moonbase, not shining and gleaming. The contrast is made all the more stark by the views of the bridge of the George W. Bush later on, which is Federation Starfleet bright and white and clean. Visuals on the moon have an almost black and white quality: not colourless, but washed out, tinted and browned like an old photograph.

Vivian Wagner. From the moment you see her slamming the table in a high-rise office and terrifying her underlings, through her gun-wielding Nazi-killing, to the moment she paces onto the bridge of the Bush wearing some utterly mad unique kickass costume with feathers framing her head, everything underlines the fact that this woman is a) off her meds, b) seriously competent, and c) not someone you want to mess with. At all.

The humour. The President of the United States is thrilled at the Nazi invasion. "All presidents who start a war in their first term get re-elected!" she says, joyfully ("I'm just like Franklin D. Roosevelt, only you know I'm not a spastic"). Renate Richter tricks her ex-fiancé into electrocuting himself on a broken lightbulb by performing the Nazi salute, in a long sequence that is at the same time both absolutely marvellous and completely ridiculous.

Nazi flying saucers. There are Nazi spaceships. And they are shaped like flying saucers.

I have a weakness for sharp, well-observed satire, and caricature that retains a core of compassion. Iron Sky does that, and does it well. It is also a film that puts plenty of time into its female characters: all the important, non-Nazi movers and shakers with screen time here, with the exception of Washington, are women. And none of them are needlessly sexualised or lessened by their womanhood.

Iron Sky is a Finnish-German-Australian co-production, whose 7.5 million euro budget was raised partly through traditional channels and partly through crowdfunding. Considering the special effects needed, it's a tiny budget—but the people behind this film really make it work. The effects are really well integrated, and the space battle is full of entertaining boom. It's proof that low budget science fiction films can have good SFX as well as smart acting.

Cleverness is only to be expected in a script co-written by Johanna Sinisalo, whose translated novel Troll: A Love Story/Not Before Sundown won the 2004 Tiptree Award. But this is a clever film, one that never takes itself too seriously but at the same time never dismisses the idea that its satire might have a real-world point. If it has a flaw, it's that this type of humour won't work for everyone. But if madcap retro SF pulp comedy appeals to you? Give Iron Sky a shot.

Maybe even if it sounds like it isn't your sort of thing. It might surprise you. I know it surprised me.

Liz Bourke is presently reading for a postgraduate degree in Classics at Trinity College, Dublin. She has also reviewed for Ideomancer and Tor.com.