To date, copper is the only monometallic catalyst that can electrochemically reduce CO into high value and energy-dense products, such as hydrocarbons and alcohols. In recent years, great efforts have been directed towards understanding how its nanoscale structure affects activity and selectivity for the electrochemical CO reduction reaction (CO RR). Furthermore, many attempts have been made to improve these two properties. Nevertheless, to advance towards applied systems, the stability of the catalysts during electrolysis is of great significance. This aspect, however, remains less investigated and discussed across the CO RR literature. In this Minireview, the recent progress on understanding the stability of copper-based catalysts is summarized, along with the very few proposed degradation mechanisms. Finally, our perspective on the topic is given.