Aspergilli have been widely used in the production of organic acids, enzymes, and secondary metabolites for almost a century. Today, several GRAS (generally recognized as safe) Aspergillus species hold a central role in the field of industrial biotechnology with multiple profitable applications. Since the 1990s, research has focused on the use of Aspergillus species in the development of cell factories for the production of recombinant proteins mainly due to their natively high secretion capacity. Advances in the Aspergillus-specific molecular toolkit and combination of several engineering strategies (e.g., protease-deficient strains and fusions to carrier proteins) resulted in strains able to generate high titers of recombinant fungal proteins. However, the production of non-fungal proteins appears to still be inefficient due to bottlenecks in fungal expression and secretion machinery. After a brief overview of the different heterologous expression systems currently available, this review focuses on the filamentous fungi belonging to the genus Aspergillus and their use in recombinant protein production. We describe key steps in protein synthesis and secretion that may limit production efficiency in Aspergillus systems and present genetic engineering approaches and bioprocessing strategies that have been adopted in order to improve recombinant protein titers and expand the potential of Aspergilli as competitive production platforms.