Multiphase solidification in multicomponent alloys is pertinent to many commercial materials and industrial processes, while also raising challenging questions from a fundamental point of view. Within the past few years, research activities dedicated to multiphase solidification of ternary and multicomponent alloys experienced considerable amplification. This paper gives an overview of our present understanding in this field and the experimental techniques and theoretical methods research relies on. We start with an introduction to thermodynamic databases and computations and emphasize the importance of thermophysical property data. Then, we address pattern formation during coupled growth in ternary alloys and cover microstructure evolution during successive steps of phase formation in solidifying multicomponent alloys. Subsequently, we review advances made in phase field modeling of multiphase solidification in binary and multicomponent alloys, including various approaches to crystal nucleation and growth. Concluding, we address open questions and outline future prospects on the basis of a close interaction among scientists investigating the thermodynamic, thermophysical and microstructural properties of these alloys.