  We develop a comprehensive framework for analyzing full record statistics,
covering record counts $M(t_1), M(t_2), \ldots$, and their corresponding
attainment times $T_{M(t_1)}, T_{M(t_2)}, \ldots$, as well as the intervals
until the next record. From this multiple-time distribution, we derive general
expressions for various observables related to record dynamics, including the
conditional number of records given the number observed at a previous time and
the conditional time required to reach the current record, given the occurrence
time of the previous one. Our formalism is exemplified by a variety of
stochastic processes, including biased nearest-neighbor random walks,
asymmetric run-and-tumble dynamics, and random walks with stochastic resetting.
