Nowadays, bioprinting is rapidly evolving and hydrogels are a key component for its success. In this sense, synthesis of hydrogels, as well as bioprinting process, and cross-linking of bioinks represent different challenges for the scientific community. A set of unified criteria and a common framework are missing, so multidisciplinary research teams might not efficiently share the advances and limitations of bioprinting. Although multiple combinations of materials and proportions have been used for several applications, it is still unclear the relationship between good printability of hydrogels and better medical/clinical behavior of bioprinted structures. For this reason, a PRISMA methodology was conducted in this review. Thus, 1,774 papers were retrieved from PUBMED, WOS, and SCOPUS databases. After selection, 118 papers were analyzed to extract information about materials, hydrogel synthesis, bioprinting process, and tests performed on bioprinted structures. The aim of this systematic review is to analyze materials used and their influence on the bioprinting parameters that ultimately generate tridimensional structures. Furthermore, a comparison of mechanical and cellular behavior of those bioprinted structures is presented. Finally, some conclusions and recommendations are exposed to improve reproducibility and facilitate a fair comparison of results.