Abstract Large deletions and genomic re‐arrangements are increasingly recognized as common products of double‐strand break repair at Clustered Regularly Interspaced, Short Palindromic Repeats ‐ CRISPR associated protein 9 (CRISPR/Cas9) on‐target sites. Together with well‐known off‐target editing products from Cas9 target misrecognition, these are important limitations, that need to be addressed. Rigorous assessment of Cas9‐editing is necessary to ensure validity of observed phenotypes in Cas9‐edited cell‐lines and model organisms. Here the mechanisms of Cas9 specificity, and strategies to assess and mitigate unwanted effects of Cas9 editing are reviewed; covering guide‐RNA design, RNA modifications, Cas9 modifications, control of Cas9 activity; computational prediction for off‐targets, and experimental methods for detecting Cas9 cleavage. Although recognition of the prevalence of on‐ and off‐target effects of Cas9 editing has increased in recent years, broader uptake across the gene editing community will be important in determining the specificity of Cas9 across diverse applications and organisms.