Mesenchymal stem/progenitor cells (MSCs) are key players in regenerative medicine, relying principally on their differentiation/regeneration potential, immunomodulatory properties, paracrine effects, and potent homing ability with minimal if any ethical concerns. Even though multiple preclinical and clinical studies have demonstrated remarkable properties for MSCs, the clinical applicability of MSC-based therapies is still questionable. Several challenges exist that critically hinder a successful clinical translation of MSC-based therapies, including but not limited to heterogeneity of their populations, variability in their quality and quantity, donor-related factors, discrepancies in protocols for isolation, in vitro expansion and premodification, and variability in methods of cell delivery, dosing, and cell homing. Alterations of MSC viability, proliferation, properties, and/or function are also affected by various drugs and chemicals. Moreover, significant safety concerns exist due to possible teratogenic/neoplastic potential and transmission of infectious diseases. Through the current review, we aim to highlight the major challenges facing MSCs’ human clinical translation and shed light on the undergoing strategies to overcome them.