The uptake of laser powder bed fusion for polymers has remained limited mainly because the interaction between material properties and process parameters is not well understood. The constraints of experimentally determining the optimal process parameters for new polymers in laser powder bed fusion include high expense, time-consumption, errors, and considerable effort. Hence, the need for using analytical and numerical models as alternatives. This paper starts with a summary on laser powder bed fusion of polymers, reviews the aspects of the process requiring the use of analytical and numerical tools, limitations, and possible improvements of the existing studies on the analytical models, and finally briefly explores approaches for numerical modelling of laser powder bed fusion of polymers. Some of the key aspects of the process that have been identified as being amenable to modelling include powder spreading and deposition of the layers, interaction between the laser beam and powder particles, melting and fusion of the particles, powder bed surface temperature, heat transfer through the powder, cooling phase, and the properties of printed parts. It is suggested in the study that the existing analytical and/or numerical models can be improved by increasing relevant variables (process parameters and material characteristics) used in them.