A family of rivets including both blind and bucked-type rivets made at least partially from an amorphous metal alloy. A blind rivet includes a head portion and a tail portion. At least one of the head portion and the tail portion is configured to elastically deform to secure a first member in position relative to a second member. The head portion and the tail portion may include one or more deformable legs having an interface feature configured to engage with one of the first member and the second member. A bucked-type rivet assembly includes a formable member and an anvil. The anvil is configured to thermoplastically deform the formable member proximate to the second member by passing current through an electrical circuit that includes at least one of the formable member and anvil.