  The generating series of a number of different objects studied in arithmetic
statistics can be built out of Euler products. Euler products often have very
nice analytic properties, and by constructing a meromorphic continuation one
can use complex analytic techniques, including Tauberian theorems to prove
asymptotic counting theorems for these objects. One standard technique for
producing a meromorphic continuation is to factor out copies of the Riemann
zeta function, for which a meromorphic continuation is already known.
  This paper is an exposition of the "Factorization Method" for meromorphic
continuation. We provide the following three resources with an eye towards
research in arithmetic statistics: (1) an introduction to this technique
targeted at new researchers, (2) exposition of existing works, with
self-contained proofs, that give a continuation of Euler products with constant
or Frobenain coefficients to the right halfplane ${\rm Re}(s)>0$ (away from an
isolated set of singularities), and (3) explicit statements on the locations
and orders of all singularities for these Euler products.
