When a colony of honeybees outgrows a hive, it will swarm for the purpose of selecting a new home. The swarm engages in a fascinating process (taking place in the late spring and early summer), during which the swarm’s scout bees examine the surrounding environment for new homes and report back on quality and location. This "house-hunting" process continues until a sufficient number of scouts agree on site. Swarms will very often choose the best site when many are available . In this talk I will describe stochastic site-selection models for the process. Natural questions for such a model include whether or not enough bees will reach a decision (i.e. will a be quorum reached), whether or not the process locates the best site and the rate at which decisions are reached.This is based on work from my Ph.D. thesis and continuing work-in-progress with my thesis adviser, Ed Waymire.