Melt electrospinning has been developed in the last decade as an eco-friendly and solvent-free process to fill the gap between the advantages of solution electrospinning and the need of a cost-effective technique for industrial applications. Although the benefits of using melt electrospinning compared to solution electrospinning are impressive, there are still challenges that should be solved. These mainly concern to the improvement of polymer melt processability with reduction of polymer degradation and enhancement of fiber stability; and the achievement of a good control over the fiber size and especially for the production of large scale ultrafine fibers. This review is focused in the last research works discussing the different melt processing techniques, the most significant melt processing parameters, the incorporation of different additives (e.g., viscosity and conductivity modifiers), the development of polymer blends and nanocomposites, the new potential applications and the use of drug-loaded melt electrospun scaffolds for biomedical applications.