Bone regenerative medicine is a clinical approach combining live osteoblast progenitors, such as mesenchymal stromal cells (MSCs), with a biocompatible scaffold that can integrate into host bone tissue and restore its structural integrity. Over the last few years, many tissue engineering strategies have been developed and thoroughly investigated; however, limited approaches have been translated to clinical application. Consequently, the development and clinical validation of regenerative approaches remain a centerpiece of investigational efforts towards the clinical translation of advanced bioengineered scaffolds. The aim of this review was to identify the latest clinical trials related to the use of scaffolds with or without MSCs to regenerate bone defects. A revision of the literature was performed in PubMed, Embase, and Clinicaltrials.gov from 2018 up to 2023. Nine clinical trials were analyzed according to the inclusion criteria: six presented in the literature and three reported in Clinicaltrials.gov. Data were extracted covering background trial information. Six of the clinical trials added cells to scaffolds, while three used scaffolds alone. The majority of scaffolds were composed of calcium phosphate ceramic alone, such as β-tricalcium phosphate (TCP) (two clinical trials), biphasic calcium phosphate bioceramic granules (three clinical trials), and anorganic bovine bone (two clinical trials), while bone marrow was the primary source of the MSCs (five clinical trials). The MSC expansion was performed in GMP facilities, using human platelet lysate (PL) as a supplement without osteogenic factors. Only one trial reported minor adverse events. Overall, these findings highlight the importance and efficacy of cell–scaffold constructs in regenerative medicine under different conditions. Despite the encouraging clinical results obtained, further studies are needed to assess their clinical efficacy in treating bone diseases to optimize their application.