Medieval carpenters did have access to glues. For woodworking, cheese glue (a glue made from casin from milk) was most popular, and is still used in traditional woodworking today. It's tough, elastic, and great for things like butt joints. There's also hide glues (most common is rabbit hide glue), which was also used for affixing other materials, such leather or parchment, to wood. But, mechanical joinery of various types were also extensively used. Pretty much all the traditional joinery was used in various contexts. Even nails were used, though more rarely die to cost.

Naturally, it depends on what sort of carpentry was being done. A house, ship, or a trebuchet have different requirements from a chair, chest, or shield.