Tomato yellow leaf curl virus (TYLCV) is a major pathogen of tomato crops in the Mediterranean basin, southern Asia, Africa and Central America whose worldwide spread continually enhances its potential impact on farmers. TYLCV is a name given to a group of viral species of the genus Begomovirus, family Geminiviridae (geminiviruses), transmitted by the whitefly Bemisia tabaci, the genome of which consists of a single circular ssDNA molecule, with only one exception in which two components were identified. The genome of TYLCV encodes six open reading frames, only one of which codes for the coat protein (CP) that represents a building block of the viral particle. TYLCV, like all other members of the Geminiviridae, has geminate particles, apparently consisting of two incomplete T = 1 icosahedra joined together so as to produce a structure with 22 pentameric capsomers and 110 identical CP subunits. Close to 40 years of intensive research into TYLCV epidemics has been conducted to find solutions to the severe problem caused by this virus. So far, breeding for resistance appears to be the best approach to controlling this disease, although only partially resistant varieties are commercially available. Since it is a ssDNA virus that replicates in the host-cell nucleus, the molecular mechanisms involved in the virus’s nuclear import have been the focus of our studies in recent years and results, as well as prospects, will be discussed. This paper provides an overview of the most outstanding achievements in TYLCV research that could lead to more effective control strategies.