The house walls are staggered 2x4 studs, used to make a 10" thick final wall, so lots of room for insulation, garage walls are just 2x4.
We used 4"spray foam on all exterior walls and filled the remainder of the cavity with cellulose insulation. The spray foam makes an excellent air seal as it expands into any cracks. Then a light cloth membrane was stapled to the studs so the dense pack cellulose is contained.
There is a lot of scraping and using a really, really long sawzall blade to trim excess foam off.
Interior walls filled with dense pack to provide some soundproofing.
The last step was to do a blower door test, which pressurizes the whole house to see how much air leaks out and where. The house was tight enough that we didn't have much to track down, but I got to wander around with an IR camera and look for cold spots and a smoke pen to find any spots where air was being pulled into the house.
One of the really interesting things about the last photo is you can really see how cold the studs are (if you click to enlarge). This is the garage and is 2x4 construction, so we have a lot of thermal bridging bringing cold in. This is one of the reasons a staggered stud 2x10 wall really makes sense as that technique goes a long way to eliminating thermal bridging.