While the default behavior is a logical OR, logical AND and NOT can also be applied among tags with the + and - prefixes, as in
which translates tocat dog +fluffy +mammal -fish
You can also specify usernames, both inclusively and exclusively, as in(cat or dog) and fluffy and mammal and not fish
user:MyFavoriteArtistThis was once upon a time discussed in a tumblr post that I will totally get around to converting into a proper help topic one of these days.-user:IHateThatGuy