Snow crystals are among the most extraordinary examples of spontaneous pattern formation in nature. Despite their apparent simplicity—water vapor freezing into ice—the resulting morphologies exhibit astonishing diversity, including stellar dendrites, hollow columns, capped columns, needles, plates, and more than one hundred classified types. This paper presents a comprehensive review of the physics governing snow crystal formation, spanning multiple scales: from the molecular-level hydrogen bonding that produces the hexagonal ice lattice, through the nucleation and faceting mechanisms that shape individual crystals, to the macroscopic environmental conditions that determine final morphology. We examine the landmark contributions of Wilson Bentley, who first photographed snowflakes in 1885, and Ukichiro Nakaya, whose laboratory experiments in the 1930s produced the celebrated snow crystal morphology diagram. We then survey the current state of scientific understanding, including Kenneth Libbrecht’s structure-dependent attachment kinetics (SDAK) hypothesis, which offers a potential resolution to an 85-year-old mystery associated with the Nakaya diagram. Finally, we discuss modern laboratory growth techniques, the creation of “designer” and “identical twin” snowflakes, and the open questions that remain at the frontier of ice crystal physics.