Adaptors for interchangeably connecting any of a plurality of clamping fixtures to various beam clamp assemblies include an adaptor block or body, a fastener attached to the adaptor block for releasably securing the adaptor block to a jaw of a beam clamp assembly, and a connector on the adaptor block for releasably attaching a workpiece clamping fixture to the adaptor block. A clamping system utilizing the adaptors may include one or a plurality of different types of beam clamp assemblies, each of which may have jaws which are differently configured, one or more adaptors, each having a fastener specially configured to facilitate releasable attachment to one of the plurality of different types of beam clamp assemblies, each of the adaptors also including a connector for releasably attaching a workpiece clamping fixture to the adaptor, and one or more workpiece clamping fixtures, each clamping fixture including a connector configured to engage the connector on any of the adaptors and facilitate releasable attachment of the clamping fixture to any of the adaptors. The clamping system allows a workpiece clamping fixture to be mounted onto any of a plurality of different beam clamp assemblies having differently configured jaws to provide greater flexibility in the selection of clamping fixtures and beam clamp assemblies for performing a particular job on a particular workpiece.