Composite materials represent the evolution of material science and technology, maximizing the properties for high-end industry applications. The fields concerned include aerospace and defense, automotive, or naval industries. Additive manufacturing (AM) technologies are increasingly growing in market shares due to the elimination of shape barriers, a plethora of available materials, and the reduced costs. The AM technologies of composite materials combine the two growing trends in manufacturing, combining the advantages of both, with a specific enhancement being the elimination of the need for mold manufacturing for composites, or even post-curing treatments. The challenge of AM composites is to compete with their conventional counterparts. The aim of the current paper is to present the additive manufacturing process across different spectrums of finite element analyses (FEA). The first outcomes are building definition (support definition) and the optimization of deposition trajectories. In addition, the multi-physics of melting/solidification using computational fluid dynamics (CFD) are performed to predict the fiber orientation and extrusion profiles. The process modelling continues with the displacement/temperature distribution, which influences porosity, warping, and residual stresses that influence characteristics of the component. This leads to the tuning of the technological parameters, thus improving the manufacturing process.