Human stem cells harbor significant potential for basic and clinical translational research as well as regenerative medicine. Currently ~ 3000 adult and ~ 30 pluripotent stem cell-based, interventional clinical trials are ongoing worldwide, and numbers are increasing continuously. Although stem cells are promising cell sources to treat a wide range of human diseases, there are also concerns regarding potential risks associated with their clinical use, including genomic instability and tumorigenesis concerns. Thus, a deeper understanding of the factors and molecular mechanisms contributing to stem cell genome stability are a prerequisite to harnessing their therapeutic potential for degenerative diseases. Chemical and physical factors are known to influence the stability of stem cell genomes, together with random mutations and Copy Number Variants (CNVs) that accumulated in cultured human stem cells. Here we review the activity of endogenous transposable elements (TEs) in human multipotent and pluripotent stem cells, and the consequences of their mobility for genomic integrity and host gene expression. We describe transcriptional and post-transcriptional mechanisms antagonizing the spread of TEs in the human genome, and highlight those that are more prevalent in multipotent and pluripotent stem cells. Notably, TEs do not only represent a source of mutations/CNVs in genomes, but are also often harnessed as tools to engineer the stem cell genome; thus, we also describe and discuss the most widely applied transposon-based tools and highlight the most relevant areas of their biomedical applications in stem cells. Taken together, this review will contribute to the assessment of the risk that endogenous TE activity and the application of genetically engineered TEs constitute for the biosafety of stem cells to be used for substitutive and regenerative cell therapies.