We integrate search theory into an equilibrium framework in a new way and argue that the result is a simple but powerful tool for understanding many issues related to bilateral matching. We assume for much of what we do that utility is less than perfectly transferable. This turns out to generate multiple equilibria that do not arise in a standard model, with transferable utility, unless one adds increasing returns. We also provide simple conditions for uniqueness that apply to models with or without transferable utility or increasing returns. Examples, applications, and extensions are discussed.