  We formulate a general theory of wave-particle duality for many-body quantum
states, which quantifies how wave- and particle-like properties balance each
other. Much as in the well-understood single-particle case, which-way
information -- here on the level of many-particle paths -- lends
particle-character, while interference -- here due to coherent superpositions
of many-particle amplitudes -- indicates wave-like properties. We analyze how
many-particle which-way information, continuously tunable by the level of
distinguishability of fermionic or bosonic, identical and possibly interacting
particles, constrains interference contributions to many-particle observables
and thus controls the quantum-to-classical transition in many-particle quantum
systems. The versatility of our theoretical framework is illustrated for
Hong-Ou-Mandel- and Bose-Hubbard-like exemplary settings.
