With respect to other fields, bone tissue engineering has significantly expanded in recent years, leading not only to relevant advances in biomedical applications but also to innovative perspectives. Polycaprolactone (PCL), produced in the beginning of the 1930s, is a biocompatible and biodegradable polymer. Due to its mechanical and physicochemical features, as well as being easily shapeable, PCL-based constructs can be produced with different shapes and degradation kinetics. Moreover, due to various development processes, PCL can be made as 3D scaffolds or fibres for bone tissue regeneration applications. This outstanding biopolymer is versatile because it can be modified by adding agents with antimicrobial properties, not only antibiotics/antifungals, but also metal ions or natural compounds. In addition, to ameliorate its osteoproliferative features, it can be blended with calcium phosphates. This review is an overview of the current state of our recent investigation into PCL modifications designed to impair microbial adhesive capability and, in parallel, to allow eukaryotic cell viability and integration, in comparison with previous reviews and excellent research papers. Our recent results demonstrated that the developed 3D constructs had a high interconnected porosity, and the addition of biphasic calcium phosphate improved human cell attachment and proliferation. The incorporation of alternative antimicrobials—for instance, silver and essential oils—at tuneable concentrations counteracted microbial growth and biofilm formation, without affecting eukaryotic cells’ viability. Notably, this challenging research area needs the multidisciplinary work of material scientists, biologists, and orthopaedic surgeons to determine the most suitable modifications on biomaterials to design favourable 3D scaffolds based on PCL for the targeted healing of damaged bone tissue.