A specification theory combines notions of specifications and implementations with a satisfaction relation, a refinement relation and a set of operators supporting stepwise design. We develop a complete specification framework for real-time systems using Timed I/O Automata as the specification formalism, with the semantics expressed in terms of Timed I/O Transition Systems. We provide constructs for refinement, consistency checking, logical and structural composition, and quotient of specifications -- all indispensable ingredients of a compositional design methodology. The theory is backed by rigorous proofs and is being implemented in the open-source tool ECDAR.