  The goal of this paper is to demystify the role played by the Reedy category
axioms in homotopy theory. With no assumed prerequisites beyond a healthy
appetite for category theoretic arguments, we present streamlined proofs of a
number of useful technical results, which are well known to folklore but
difficult to find in the literature. While the results presented here are not
new, our approach to their proofs is somewhat novel. Specifically, we reduce
the much of the hard work involved to simpler computations involving weighted
colimits and Leibniz (pushout-product) constructions. The general theory is
developed in parallel with examples, which we use to prove that familiar
formulae for homotopy limits and colimits indeed have the desired properties.
