How are aircraft depainted? There are several questions about livery changes and livery in general on this website. Yet, I fail to find information about paint removal.

As a routine maintenance for an airframe that can live for up to 30 years, livery is redone several time as explained here. When changing painting, it should be preferable to remove the old one (I'm mostly thinking about weight as a big airliners has a lot a surface to paint). Moreover, I imagine that for military aircraft changing their operation theater, paint must be redone to adapt camouflage, and thus accumulating many layers of paint may have consequences.

Given material and other aviation-specific constraints, I also imagine there are special techniques to handle any intervention on the airframe.

Is this paint removal done and if so, how?
Paint stripper. Lots of paint stripper. 
(originally I said thinner, but I have been corrected, it's more accurately called stripper)

Seriously though, it's actually not too different to other things that you paint. You need to spray on paint stripper. But, just like when painting the aircraft, it's imperative that you cover up all the delicate systems on the aircraft fuselage.

See here: 
                
            

Also, I think it would be rare to paint a new livery over and existing one without first removing the old paint (maybe only if you were just changing small details), because covering an aircraft in paint weighs A LOT. For a 747 or 777 sized aircraft the paint job can weigh over 1000lbs 

Carrying that around costs fuel and fuel costs a lot!