  Statistical matching is an effective method for estimating causal effects in
which treated units are paired with control units with ``similar'' values of
confounding covariates prior to performing estimation. In this way, matching
helps isolate the effect of treatment on response from effects due to the
confounding covariates. While there are a large number of software packages to
perform statistical matching, the algorithms and techniques used to solve
statistical matching problems -- especially matching without replacement -- are
not widely understood. In this paper, we describe in detail commonly-used
algorithms and techniques for solving statistical matching problems. We focus
in particular on the efficiency of these algorithms as the number of
observations grow large. We advocate for the further development of statistical
matching methods that impose and exploit ``sparsity'' -- by greatly restricting
the available matches for a given treated unit -- as this may be critical to
ensure scalability of matching methods as data sizes grow large.
