Understanding advective-diffusive dispersal of trace substances in environmental fluids like the global ocean is a ubiquitous challenge in geophysics. Since the turn of the millennium, substantial progress has been made in the theory, implementation in models, and application of such tracers in oceanography. For the first time, this progress is reviewed here in a synthetic way. We focus on tracer techniques in ocean models, including naturally-occurring and hypothetical tracers that diagnose timescale information, and we emphasize the connection to the Green's function that solves the advection-diffusion equation. Implementation of these techniques in ocean models is explained in an accessible way. We present example applications of these techniques to questions concerning ocean circulation, transport of biogeochemicals, and paleooceanography, including future opportunities.