  We develop the general framework of virtual resource distillation -- an
alternative distillation strategy proposed in [Phys. Rev. Lett. 132, 050203
(2024)], which extends conventional quantum resource distillation by
integrating the power of classical postprocessing. The framework presented here
is applicable not only to quantum states, but also dynamical quantum objects
such as quantum channels and higher-order processes. We provide a general
characterization and benchmarks for the performance of virtual resource
distillation in the form of computable semidefinite programs as well as several
operationally motivated quantities. We apply our general framework to various
concrete settings of interest, including standard resource theories such as
entanglement, coherence, and magic, as well as settings involving dynamical
resources such as quantum memory, quantum communication, and non-Markovian
dynamics. The framework of probabilistic distillation is also discussed.
