Solidification cracking is a weld defect common to certain susceptible alloys rendering many of them unweldable. It forms and grows continuously behind a moving weld pool within the two phase mushy zone and involves a complex interaction between thermal, metallurgical and mechanical factors. Despite decades long efforts to investigate weld solidification cracking, there remains a significant lack of understanding regarding its underlying mechanisms. Criteria developed to evaluate alloy weldability will be examined in terms of proposed solidification cracking models. Crack initiation is discussed in terms of different criteria: critical stress to fracture the interdendritic liquid, critical strain to exceed the mushy zone ductility and critical hydrogen content to nucleate and grow a pore. Crack growth has been characterised in terms of a critical stress to fracture the liquid film surrounding a grain and critical strain rate interdependent with liquid feeding of the mushy zone opening. Experimental data to form a weld solidification crack are compiled, revealing the considerable amount of information available in the literature on this topic.