In the current review, an exceptional view on the multi-scale integrated computational modelling and data-driven methods in the Additive manufacturing (AM) of metallic materials in the framework of integrated computational materials engineering (ICME) is discussed. In the first part of the review, process simulation (P-S linkage), structure modelling (S-P linkage), property simulation (S-P linkage), and integrated modelling (PSP and PSPP linkages) are elaborated considering different physical phenomena (multi-physics) in AM and at micro/meso/macro scales (multi-scale modelling). The second part provides an extensive discussion of a data-driven framework, which involves extracting existing data from databases and texts, data pre-processing, high throughput screening, and, therefore, database construction. A data-driven workflow that integrates statistical methods, including ML, artificial intelligence (AI), and neural network (NN) models, has great potential for completing PSPP linkages. This review paper provides an insight for both academic and industrial researchers, working on the AM of metallic materials.