There are many results that give upper bounds on the number of number fields of given degree and bounded discriminant, possibly with some extra structure (e.g. Galois group) or ordered in a different way. In this talk, we'll overview these results, how they fit together, and how to best think about obtaining upper bounds for a given family of number fields. We'll also aim to sell the problem of obtaining "inertial multiplicity bounds" for families of number fields. We expect this perspective will be useful both this workshop and more broadly.