  We study the nature of cluster selection in Sunyaev-Zel'dovich (SZ) surveys,
focusing on single frequency observations and using Monte Carlo simulations
incorporating instrumental effects, primary cosmic microwave background (CMB)
anisotropies and extragalactic point sources. Clusters are extracted from
simulated maps with an optimal, multi-scale matched filter. We introduce a
general definition for the survey selection function that provides a useful
link between an observational catalog and theoretical predictions. The
selection function defined over the observed quantities of flux and angular
size is independent of cluster physics and cosmology, and thus provides a
useful characterization of a survey. Selection expressed in terms of cluster
mass and redshift, on the other hand, depends on both cosmology and cluster
physics. We demonstrate that SZ catalogs are not simply flux limited, and
illustrate how incorrect modeling of the selection function leads to biased
estimates of cosmological parameters. The fact that SZ catalogs are not flux
limited complicates survey ``calibration'' by requiring more detailed
information on the relation between cluster observables and cluster mass.
