Icosahedral nanocrystals of noble metals have received ever increasing interests in recent years owing to their unique features such as the size-dependent distribution of strain fields and the presence of a large number of twin boundaries. In this review, we start with a brief introduction to the strain field distribution on an icosahedral nanocrystal and then we discuss the size-dependent structural thermodynamics, together with remarks on the synthetic approaches to icosahedral nanocrystals of various noble metals in high purity. The recent breakthroughs in synthesis can be attributed to a strong correlation between the kinetics of reduction and the way atoms are assembled in nuclei during homogenous nucleation. We aim to provide a brief account of new developments while highlighting the key experimental parameters that give rise to icosahedral nanocrystals. We focus on monometallic systems based on Au, Ag, Pd, Pt, and Rh, along with some bimetallic systems. At the end, we showcase the performance of icosahedral nanocrystals towards catalytic and photonic applications, and offer some perspectives on future directions.