Non-Humean theories of natural necessity invoke modallyladen primitives to explain why nature exhibits lawlike regularities. However, they vary in the primitives they posit and in their subsequent accounts of laws of nature and related phenomena (including natural properties, natural kinds, causation, counterfactuals, and the like). This article provides a taxonomy of non-Humean theories, discusses influential arguments for and against them, and describes some ways in which differences in goals and methods can motivate different versions of non-Humeanism (and, for that matter, Humeanism). In short, this article provides an introduction to non-Humeanism concerning the metaphysics of laws of nature and natural necessity.