Metal additive manufacturing (MAM) harbors the potential for controlled and optimized material microstructures, with the ability to design and build metal components specifically tailored to their application. The various processes of MAM, such as electron beam melting (EBM) and powder bed fusion (PBF), typically involve rapid solidification which strongly influences the morphology and growth rate of the microstructure. The modification of process parameters (scan speed, laser power, cooling rate, imposed bed temperature gradient, etc.) allows for the control of dendrite morphology, and henceforth the macroscopic properties of the material (mechanical strength, creep resistance, high-temperature resistance, etc.). In situ observation of dendritic solidification is challenging due to the multiphysics and multiple time and length scales involved. Instead, numerical modeling (specifically the phase-field method) has been hailed as a promising alternative to understand and study dendritic evolution during solidification. Here we present a coupled finite difference—lattice Boltzmann phase-field model (FD-LB PFM) to simulate the dynamics of solidification during MAM. The proposed model includes transient simulations of the evolution of the phase-field, melt flow, species concentration field, and temperature field. The work begins with a detailed review of the elementary and recent works related to phase-field modeling. The proposed model is then detailed and applied to both single crystal and multicrystal solidification problems to demonstrate its accuracy and applicability. Simulations are verified against several representative problems in previous literature (including realistic alloys such as Al-3wt%Cu and aluminum alloy A356) to demonstrate the efficacy of using PFM for effective MAM modeling.