In recent years, crystal structure prediction (CSP) methods have developed considerably to tackle the challenge of predicting putative crystal structures of molecular and atomistic crystals. While definitive and routine prediction of structures and properties remains difficult, recent progress means that CSP calculations can already impact on crystal engineering, pharmaceutical solid-form risk assessment and screening, and materials design, as well as crystal structure determination. This chapter provides an overview of recent developments and progress in CSP methods, summarizes current approaches to performing CSP calculations, and discusses current challenges and frontiers for CSP methods and their application.