  A general approach to transference principles for discrete and continuous
operator (semi)groups is described. This allows to recover the classical
transference results of Calder\'on, Coifman and Weiss and of Berkson, Gillespie
and Muhly and the more recent one of the author. The method is applied to
derive a new transference principle for (discrete and continuous) operator
semigroups that need not be groups. As an application, functional calculus
estimates for bounded operators with at most polynomially growing powers are
derived, culminating in a new proof of classical results by Peller from 1982.
The method allows a generalization of his results away from Hilbert spaces to
$\Ell{p}$-spaces and --- involving the concept of $\gamma$-boundedness --- to
general Banach spaces. Analogous results for strongly-continuous one-parameter
(semi)groups are presented as well. Finally, an application is given to
singular integrals for one-parameter semigroups.
