In recent years the theory of structured ring
spectra (formerly known as A$_{\infty}$- and
E$_{\infty}$-ring spectra) has been simplified
by the discovery of categories of spectra with
strictly associative and commutative smash products.
Now a ring spectrum can simply be defined as a
monoid with respect to the smash product in one
of these new categories of spectra. In this paper
we provide a general method for constructing model
category structures for categories of ring, algebra,
and module spectra. This provides the necessary
input for obtaining model categories of symmetric
ring spectra, functors with smash product,
$\Gamma$-rings, and diagram ring spectra.
Algebraic examples to which our methods apply
include the stable module category over the group
algebra of a finite group and unbounded chain
complexes over a differential graded algebra. 1991 Mathematics Subject Classification: primary 55U35; secondary 18D10.