The vehicles have been identified as accurately as possible, by comparing visible features with drawings, photographs and lists of modifications. Whenever possible, original German vehicle names are used. In order to keep names consistent, however, some liberties have been taken.
As an example, early in the war, the Sturmgeschütz III was officially called Sturmgeschütz 40. Rather than using two different names for what is, essentially, the same vehicle, Sturmgeschütz III is used throughout.
The date on the photograph is usually added by the photographer. German war photographers dated their photographs, so if the exact date is stated, there's a good chance it's taken by a war photographer. Private photographs are also sometimes dated, though usually only with a year and sometimes a month.
Sometimes, even though the photograph isn't dated explicitly, the date can still be derived from the scene. For example, photographs from the German invasion of Poland can reasonably be assumed to be from September 1939. An assumed date is only shown if there's a high degree of certainty.
I wish to thank the following people for helping me identify vehicles, locations and people: