Over the last decade, CRISPR has revolutionized drug development due to its potential to cure genetic diseases that currently do not have any treatment. CRISPR was adapted from bacteria for gene editing in human cells in 2012 and, remarkably, only 11 years later has seen it's very first approval as a medicine for the treatment of sickle cell disease and transfusion-dependent beta-thalassemia. However, the application of CRISPR systems is associated with unintended off-target and on-target alterations (including small indels, and structural variations such as translocations, inversions and large deletions), which are a source of risk for patients and a vital concern for the development of safe therapies. In recent years, a wide range of methods has been developed to detect unwanted effects of CRISPR-Cas nuclease activity. In this review, we summarize the different methods for off-target assessment, discuss their strengths and limitations, and highlight strategies to improve the safety of CRISPR systems. Finally, we discuss their relevance and application for the pre-clinical risk assessment of CRISPR therapeutics within the current regulatory context.