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A general approach to transference principles for discrete and continuousoperator (semi)groups is described. This allows to recover the classicaltransference results of Calder\'on, Coifman and Weiss and of Berkson, Gillespieand Muhly and the more recent one of the author. The method is applied toderive a new transference principle for (discrete and continuous) operatorsemigroups that need not be groups. As an application, functional calculusestimates for bounded operators with at most polynomially growing powers arederived, 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 --- togeneral Banach spaces. Analogous results for strongly-continuous one-parameter(semi)groups are presented as well. Finally, an application is given tosingular integrals for one-parameter semigroups.

Transference Principles for Semigroups and a Theorem of Peller