Sugarcane is a lignocellulosic crop which is used to produce sugar in sugarcane processing industries. Globally, sugarcane processing industries generate solid and liquid wastes amounting to more than 279 million tons per annum and by-products; namely, trash, bagasse, mill mud, and molasses. The valorisation of waste and by-products has recently increased and is playing a significant role in achieving policies and goals associated with circular bioeconomy and sustainable development. For the valorisation of sugarcane processing industry waste and by-products, a number of technologies are well established and in use, while other innovative technologies are still ongoing through research and development with promising futures. These by-products obtained from sugarcane processing industries can be converted into biofuels like hydrogen and methane via anaerobic digestion. Molasses belongs to the first-generation (1G) waste, while trash, bagasse, and mill mud belong to second-generation (2G) waste. Various studies have been carried out in converting both first- and second-generation sugarcane processing industry wastes into renewable energy, exploiting anaerobic digestion (AD) and dark fermentation (DF). This review emphasises the various factors affecting the AD and DF of 1G and 2G sugarcane processing industry wastes. It also critically addresses the feasibility and challenges of operating a two-stage anaerobic digestion process for hydrogen and methane production from these wastes.