In the rapidly evolving field of additive manufacturing (AM), the predictability of part properties is still challenging due to the inherent multiphysics complexity of the technology. This results in time-consuming and costly experimental guess-and-check approaches for manufacturing each individual design. Through synthesising advancements in the field, this review argues that numerical modelling is instrumental in mitigating these challenges by working in tandem with experimental studies. Unique hierarchical microstructures induced by extreme AM process conditions- including melt pool patterns, grains, cellular-dendritic substructures, and precipitates-affect the final part properties. Therefore, the development of microstructure-informed mechanical models becomes vital. Our review of numerical studies explores various modelling approaches that consider the microstructural features explicitly and offers insights into multiscale stress-strain analysis across diverse materials fabricated by powder bed fusion AM. The literature indicates a growing consensus on the key role of multiscale integrated process-structure-property-performance (PSPP) modelling in capturing the complexity of AM-produced materials. Current models, though increasingly sophisticated, still tend to relate only two elements of the PSPP chain while often focusing on a single scale. This emphasises the need for integrated PSPP approaches validated by a solid experimental base. The PSPP paradigm for AM, while promising as a concept, is still in its infantry, confronting multifaceted challenges that require in-depth, multidisciplinary expertise. These challenges range from accounting for multiphysics phenomena (e.g., advanced laser-material interaction) and their interplay (thermo-mechanical and microstructural evolution for simulating Type II residual stresses), accurately defined assumptions (e.g., flat molten surface during AM or purely epitaxial solidification), and correctly estimated boundary conditions for each element of the PSPP chain up to the need to balance the model's complexity and detalisation in terms of both multiphysics and discretisation with efficient multitrack and multilayer simulations. Efforts in bridging these gaps would not only improve predictability but also expedite the development and certification of new AM materials.