  Current-biased Josephson junctions exhibit hysteretic transitions between
dissipative and superconducting states as characterized by switching and
retrapping currents. Here, we develop a theory for diode-like effects in the
switching and retrapping currents of weakly-damped Josephson junctions. We find
that while the diode-like behavior of switching currents is rooted in
asymmetric current-phase relations, nonreciprocal retrapping currents originate
in asymmetric quasiparticle currents. These different origins also imply
distinctly different symmetry requirements. We illustrate our results by a
microscopic model for junctions involving a single magnetic atom. Our theory
provides significant guidance in identifying the microscopic origin of
nonreciprocities in Josephson junctions.
