The humble snowflake presents something of an embarrassment to the scientific community, as it is not yet possible to explain its structure at even a superficial level. It is especially challenging to understand the full menagerie of exotic snow crystal morphologies that arise as a function of temperature and supersaturation. Physically realistic computational growth models are beginning to show promise, but they cannot yet reproduce even basic laboratory experiments. In large part, this unfortunate situation exists because the ice crystal exhibits a complex surface structure accompanied by a remarkably temperature-dependent, highly anisotropic molecular attachment kinetics. I will describe the phenomenology of snow crystal growth provided by laboratory measurements, and I will present a new physical model that may finally provide a comprehensive picture of the underlying molecular processes.