This chapter describes the structures, phases, and phase transformations observed in metals and alloys as they solidify and cool to lower temperatures. It begins with a review of the solidification process, covering nucleation, grain growth, and the factors that influence grain morphology. It then discusses the concept of solid solutions, the difference between substitutional and interstitial solid solubility, the effect of alloying elements, and the development of intermetallic phases. The chapter also covers the construction and use of binary and ternary phase diagrams and describes the helpful information they contain.