In the last decade, substantial progress has been made towards standardizing the syntax of graph query languages, and towards understanding their semantics and complexity of evaluation. In this paper, we consider temporal property graphs (TPGs) and propose temporal regular path queries (TRPQs) that incorporate time into TPG navigation. Starting with design principles, we propose a natural syntactic extension of the MATCH clause of popular graph query languages. We then formally present the semantics of TRPQs, and study the complexity of their evaluation. We show that TRPQs can be evaluated in polynomial time if TPGs are time-stamped with time points, and identify fragments of the TRPQ language that admit efficient evaluation over a more succinct interval-annotated representation. Finally, we implement a fragment of the language in a state-of-the-art dataflow framework, and experimentally demonstrate that TRPQ can be evaluated efficiently.