In recent years, metal Additive manufacturing (AM) and remanufacturing (RM) have increasingly penetrated various industrial sectors, driven by their potential to enhance functionality, boost productivity, and strengthen competitiveness. However, the rapid melting and solidification processes of metal AM/RM are accompanied by high temperature gradients, which inevitably result in significant thermal stress and potential process-induced cracks. Cracks can seriously affect the strength and fatigue performance of printed metal materials, therefore, it is of great importance to control process-induced cracks in metal AM/RM. Current crack suppression/elimination methods include: (1) adjusting the material compositions to avoid compositional defects by reducing the effects of oxidation, loss of alloying elements and microscopic segregation; (2) optimizing process parameters to control the heat input and its sequence; (3) preheating and post-processing to reduce the thermal gradient; and (4) introducing auxiliary energy fields to improve the forming process, etc. This paper provided a comprehensive review of the process-induced crack control strategies in metal AM/RM, and described in detail the effects of material systems, process parameters, auxiliary energy fields, and post-heat treatment in inhibiting cracks. The strengths and weaknesses of the current crack control approaches were discussed, and the future research concerns for crack control in metal AM/RM were provided.