Time-reparametrization-invariant dynamics of relativistic systems

This review is devoted to the description of the reparametrization-invarian t dynamics of relativistic systems (special relativity, strings, and genera l relativity) obtained by resolving constraints and constructing equivalent unconstrained systems. The constraint-shell actions allow us to give clear mathematical definitions of measurable quantities in both classical and qu antum theories, such as the geometric time interval, the dynamic evolution parameter in the world space of dynamic variables, or the energy density an d the holomorphic (particle-like) variables in general relativity.