This one's pretty straightforward. Apparently the Euro cars have a different airbox with a cylindrical filter, and you can change it without removing the airbox. I took a few pictures when I changed the filter on my 128i in case they're helpful to anyone.
The only parts you'll need are a new air filter element, and tools include a 10mm socket, flat head screwdriver or small socket & extension, a shop vac or compressed air or a soft paintbrush (for cleaning), a plastic pry tool if you care about not scratching stuff, and shop towels. Please note that the captions correspond to the image below, not above.
1. remove the two 10mm bolts (#1). #2 shows the MAF sensor location, and #2 shows the hose clamp which holds the rubber intake boot to the back of the airbox.
2. Carefully pry up the tab with a plastic pry tool, then slide the wiring plug out. I wrapped the plug in painters tape to keep dust and dirt out, but that's probably overkill.
3. Clean the area around the boot well. You want to do everything you can here to avoid dropping dirt, dust, and grit into the intake piping. Then loosen the hose clamp sufficiently.
4. Moving to the front of the car, there's a flexible connector where the airbox joins the front air diverter. Carefully pry up the tabs on the left and right side, then squeeze the airbox section to release the tabs.
5. Once the tabs are free you can pull back the flexible connector a bit. It's not massively flexible but it'll move enough to let you get the airbox out.
6. The airbox has a lip underneath it that sticks out another third of an inch or so. This makes it a bit more tricky to clear the flexible connector but it's not too bad. Lift this side of the airbox up so it's resting on the section still attached to the car.
7. With the hose clamp loosened, carefully slide the intake boot back off the airbox. Now the airbox is no longer attached to the car, but it still takes a bit of wiggling to get it removed.
8. I found that rotating the airbox back slightly and lifting it out was easiest. You have to wiggle the tab where you removed the bolts because that sits underneath a bit of the bodywork. There's no additional hidden clips etc. so once you've got it free just lift it out of the car.
9. Now the airbox is removed, clean up the intake boot and the front air diverter box connections. Do not use compressed air for this. I used shop towels and some lint roller sheets. A clean shop vac would also work very well I think. If you're going way overboard here or are working outdoors, I'd cover the open intake boot with a ziploc and rubber band.
10. With the airbox removed, set it down on something to protect it and
slacken the bolts around the edge with a T25 torx bit.
You don't have to remove the bolts all the way as I put on the image, they will remain in the 'lid' of the airbox. Be careful not to get the MAF sensor dirty as these are pretty sensitive. I was going to clean it with CRC MAF cleaner but the new design meant I'd have had to remove it completely.
11. With the lid removed, take out the replaceable air filter (mine was yellow paper with orange rubber trim, you can't miss it
. Interestingly on this car it had what I assume is a secondary air filter, much like a household AC filter that was part of the lid. I didn't see any way to remove or clean this so I left it alone.
12. When I removed the air filter element, I found a lot of debris on the 'dirty' (unfiltered) side of the airbox. I decided to clean this out, again a paintbrush and/or shop vac/compressed air will work. You could probably even wash it if you had the time to let it dry thoroughly. Clean the mating surfaces of the airbox and the lid to make sure there's no grit or dirt that could compromise the seal.
Once you've got that clean, install the new air filter, making sure it's seated properly the whole way around. It's quite snug and I had to wiggle it a bit around the narrow end to get the paper element fully seated. Refit the lid and tighten all the torx bolts, going in a diagonal pattern. Don't overtighten these as you could deform the airbox.
Once the airbox is back together, rotate it back into the car by tilting the back down. Make sure the rubber intake boot isn't forced down by the airbox, try and pull it back so it's in roughly the right place. Reconnect the flexible coupling on the front side of the airbox, and wiggle the airbox to get the bolt tabs back in the right place. I didn't reinstall the bolts yet but you probably could.
Working on the back of the airbox, pull the intake boot back onto it's mounting point. This requred a bit of patience. If you can, reach underneath to make sure it's seated on the underside too. A small mirror might help here if you can't reach. Hold the intake boot up against the airbox, and tighten the hose clamp. There's two rubber locating blocks on the boot, make sure you get the clamp screw inbetween them. I assume this solves the problem on older bmw's where these clamps were tightened up before the engine was installed, then were very difficult to access after the fact. Nice feature.
Reconnect the MAF wiring plug, ensuring the tab snaps into place. Doesn't require much force at all. You could grease the outside of the rubber seal on the plug with a little silicone grease if you wanted to or live somewhere very wet.
Once you've checked it's all back in place correctly, reinstall the two bolts if you didn't already. Again these don't need to be super tight as they simply hold the rubber mounts in place. You're done!
Here's what my original air filter looked like after 17,000 miles. Quite a lot of visible dirt so glad I changed it out.
Note: the DIY ends here, all the pictures below are just the attached images used in the post.