How does this work?

I assume you booked a ticket all the way through to Munich and did not book the tickets separately through different airlines? If so, when you arrive in London, your bags will be transferred to the new flight, nothing required to be done by you. The best case scenario is that your departing flight will be in the same international transit area, and you will be able to just walk to your gate and wait to board. You may very well have to change terminals, which in some cases requires going through Security again, where you will have your passport checked as ID, your bags x-rayed, and on your way. London Heathrow seems to have been under construction forever, so it seems different every time I go through there. You would not go through Immigration control for the UK, since technically you will not enter the country. Once you hit Munich, you will need to go through EU Passport Control, then claim your bags, if you have nothing to declare to Customs, then walk out the door, if so, then find the Customs area near the exit.

My experience is that you always have to go through security when you transfer at LHR, also when staying in the same terminal. There may be exceptions, though. Transfers between terminals at London Heathrow is via an airside bus. Although LHR is a huge airport, and can be somewhat overwhelming, I find it clearly marked and the colour coded signs help alot. Know which terminal you arrive to and which terminal you depart from and follow the purple flight connection signs.

But to answer your questions: No, you do not go through immigration or customs in London, only security. You go through immigration and customs in Munich. This is because the UK is not part of the Schengen-area, so the UK has their own immigration system. Had your flight been with a connection in a Schengen country (e.g. a connection in Amsterdam, Paris or Frankfurt), you would have cleared immigration at your connecting point. Your onward flight would then have been an intra Schengen flight, which is almost like a domestic flight.

So, when I change planes in Copenhagen on the way to Helsinki, I'll go through immigration but not customs? Are the lines fairly short there (for EU passports)?

@Kathy, are you goting to Helsinki from the US or another European country?
I've flown from Germany to Amsterdam thru Copenhagen and there were no formalities at all-depends on where you are coming from. Great stores in the Copenhagen airport, and substantial prices for food and drink. Busy airport, found the SAS transit center was quieter and had more available seats than the other public areas when we were there.

@Melissa - I'm coming from the US. I'll leave the US on my US passport, and enter Europe on my UK one. I have 2+ hours to make the connection, if all goes to schedule.

@Kathy. If you arrive to Copenhagen on a direct flight from the US, and travel onwards within Europe, yes, you will enter the Schengen zone in Copenhagen, which means that you will pass immigration control here. Copenhagen does not have that many long haul flights and thus, not many immigration booths, and lines are normally not that long, but it also means, that two or three simultaneous flights arriving can clog up things quite abit. You could say theat the fact that there are few flights means that the load is quite unevenly distributed. At certain times the booths are litteraly deserted, then two flights come in at the same time and there are long lines. Customs in Europe is very light, normally just a walk through, and is performed at your final destination. In Helsinki , if there is a choice, you should choose the channel "arriving from outside EU, nothing to declare" since you origin (customs-wise) is ouside the EU.

@Christophe - thanks. Since it's all on one ticket, I should be OK anyway. (I hope.)

Customs in Europe is very light, normally just a walk through, and is performed at your final destination >> It is not that way! Customs controls are done in the first arrival at any Schengen-area airport, e.g., the airport in which your transcontinental flight arrived! A Miami-Madrid-Berlin flight will have its passengers checked for immigration at Madrid. People travelling Los Angeles-Amsterdam-Milan will pass through border control in Amsterdam. In the specific cases of passengers connecting via United Kingdom or Ireland, as such countries are not part of the common travel area of Schengen treaty, the passenger WILL face control at its final destination and MAY face also border control in London. Immigration controls for connecting passengers in London are fast.

@andre
Immigration a.k.a. passport control is at your first point of entry to the Schengen area. Customs is at your final destination. You cannot go through customs before you have your bags in hand therefore customs is always when you exit the airport, after baggage claim at your final destination. However, customs booths are often unmanned and sometimes barely noticed by passengers. Immigration at your first point of entry to the Schengen area, on the other hand, is always staffed.