Tomato yellow leaf curl (TYLC) is one of the most devastating viral diseases of cultivated tomato (Lycopersicon esculentum) in tropical and subtropical regions worldwide, and losses of up to 100% are frequent. In many regions, TYLC is the main limiting factor in tomato production. The causal agents are a group of geminivirus species belonging to the genus Begomovirus of the family Geminiviridae, all of them named Tomato yellow leaf curl virus (TYLCV) (sensu lato). There has been almost 40 years of research on TYLCV epidemics and intensive research programmes have been conducted to find solutions to the severe problem caused by these viruses. This paper provides an overview of the most outstanding achievements in the research on the TYLCV complex that could lead to more effective control strategies.