Tank museum historian here. I think I can shed some light on this, particularly post WWII.

Following the war, a massive effort got underway to get rid of all the excess tanks, ships, guns, what have you. I have an article from a Time Magazine in 1945 talking about saving a B-17 because of its history with a backdrop of dozens of Victory cargo ships waiting to be scrapped.
A lot of vehicles, like older tanks, were sold to newer countries who wanted a small military force post-war. Italy and Belgium especially took on a great number of M26 Pershing tanks after it was all over, and they were either scrapped there or sent back to the US to be scrapped when they were deemed unnecessary. Airplanes were taken apart (knew a guy whose great uncle flew in the war and had the unfortunate experience of watching HIS plane get blown up in a newsreel detailing the de-mobilization and scrapping of aircraft.) Some, like large numbers of P-51s, M4 Shermans, etc, were kept for evaluation after the war, or as short-term force multipliers, and were sold off as surplus to civilians once they weren't needed. The Russians held on to outdated equipment for a long time, mostly selling those vehicles or offering them to their new puppet states. For small arms like rifles, again, a lot of those were held onto by the government until they weren't needed anymore or outdated, and then sold off as surplus. Some guys after WWII were allowed to keep their rifles and brought it home with them.

What I always found interesting is the military vehicle buying/selling bonanza that occurred after the USSR collapsed in 1991. A lot of the "Soviet" equipment we have in our museum came from East Germany, who dropped their T-55s, T-72s and Shilka SPAAs like hot rocks once western machines were readily available.