Healthcare waste comprises the waste generated by healthcare facilities, medical laboratories and biomedical research facilities. Improper treatment of this waste poses serious risks of disease transmission to waste pickers, waste workers, health workers, patients, and the community in general through exposure to infectious agents. Poor management of the waste emits harmful and deleterious contaminants into society. However, contamination of highly contagious agents such as the COVID-19 virus has created enormous instability in healthcare waste handling and subsequent recycling because of the volume of the waste generated and its contagious nature. Several countries have adopted safety measures to combat this contamination and manage healthcare waste; however, these measures are insufficient and vary depending on the context of the country. In addition, the WHO has set out guidelines for management of healthcare waste. These guidelines are helping to manage the highly contagious healthcare waste resulting from the current pandemic. Proper healthcare waste management may add value by reducing the spread of the COVID-19 virus and increasing the recyclability of materials instead of sending them to landfill. Disinfecting and sorting out healthcare waste facilitates sustainable management and allows their utilization for valuable purposes. This review discusses the different healthcare solid waste management strategies practiced in different countries, the challenges faced during this management, and the possible solutions for overcoming these challenges. It also provides useful insights into healthcare solid waste management scenarios during the COVID-19 pandemic and a possible way forward.