Current-biased Josephson junctions exhibit hysteretic transitions between dissipative and superconducting states as characterized by switching and retrapping currents. We develop a phenomenological theory of nonreciprocal switching and retrapping in underdamped junctions within the resistively and capacitively shunted junction (RCSJ) model. We find that while the diodelike behavior of switching currents is rooted in asymmetric current-phase relations (requiring broken time-reversal symmetry), nonreciprocal retrapping currents originate in asymmetric quasiparticle currents (requiring broken particle-hole symmetry). These distinct symmetry requirements explain the observation of nonreciprocal retrapping in Josephson junctions that involve a single magnetic atom, where Yu–Shiba–Rusinov (YSR) states break particle-hole symmetry at subgap energies. Going beyond phenomenology, we show how nonreciprocity in the RCSJ model arises from a microscopic description. Essentially, the YSR states contribute significantly to the damping when the transparency of the junction is relatively large, necessitating a calculation to all orders in the tunneling amplitude. Within an adiabatic approximation, the damping reduces to the quasiparticle current evaluated at the instantaneous junction voltage—thereby inheriting YSR-induced particle–hole asymmetries in the density of states and capturing higher-order processes such as multiple Andreev reflections. Finally, we show that the accompanying fluctuations obey a generalized (nonlinear) fluctuation–dissipation relation provided temperatures are sufficiently large.