  Phase transitions in random systems are smeared if individual spatial regions
can order independently of the bulk system. In this paper, we study such
smeared phase transitions (both classical and quantum) in substitutional alloys
A$_{1-x}$B$_x$ that can be tuned from an ordered phase at composition $x=0$ to
a disordered phase at $x=1$. We show that the ordered phase develops a
pronounced tail that extends over all compositions $x<1$. Using optimal
fluctuation theory, we derive the composition dependence of the order parameter
and other quantities in the tail of the smeared phase transition. We also
compare our results to computer simulations of a toy model, and we discuss
experiments.
