  In this paper we study the semiclassical behavior of quantum states acting on
the C*-algebra of canonical commutation relations, from a general perspective.
The aim is to provide a unified and flexible approach to the semiclassical
analysis of bosonic systems. We also give a detailed overview of possible
applications of this approach to mathematical problems of both axiomatic
relativistic quantum field theories and nonrelativistic many body systems. If
the theory has infinitely many degrees of freedom, the set of Wigner measures,
i.e. the classical counterpart of the set of quantum states, coincides with the
set of all cylindrical measures acting on the algebraic dual of the space of
test functions for the field, and this reveals a very rich semiclassical
structure compared to the finite-dimensional case. We characterize the
cylindrical Wigner measures and the \emph{a priori} properties they inherit
from the corresponding quantum states.
