Additive manufacturing (AM) is a broad definition of various techniques to produce layer-by-layer objects made of different materials. In this paper, a comprehensive review of laser-based technologies for polymers, including powder bed fusion processes [e.g. selective laser sintering (SLS)] and vat photopolymerisation [e.g. stereolithography (SLA)], is presented, where both the techniques employ a laser source to either melt or cure a raw polymeric material. The aim of the review is twofold: (1) to present the principal theoretical models adopted in the literature to simulate the complex physical phenomena involved in the transformation of the raw material into AM objects and (2) to discuss the influence of process parameters on the physical final properties of the printed objects and in turn on their mechanical performance. The models being presented simulate: the thermal problem along with the thermally activated bonding through sintering of the polymeric powder in SLS; the binding induced by the curing mechanisms of light-induced polymerisation of the liquid material in SLA. Key physical variables in AM objects, such as porosity and degree of cure in SLS and SLA respectively, are discussed in relation to the manufacturing process parameters, as well as to the mechanical resistance and deformability of the objects themselves. Graphic abstract