Many plant viruses depend on insect vectors for their transmission and dissemination. The whitefly Bemisia tabaci (Hemiptera: Aleyrodidae) is one of the most important virus vectors, transmitting more than four hundred virus species, the majority belonging to begomoviruses (Geminiviridae), with their ssDNA genomes. Begomoviruses are transmitted by B. tabaci in a persistent, circulative manner, during which the virus breaches barriers in the digestive, hemolymph, and salivary systems, and interacts with insect proteins along the transmission pathway. These interactions and the tissue tropism in the vector body determine the efficiency and specificity of the transmission. This review describes the mechanisms involved in circulative begomovirus transmission by B. tabaci, focusing on the most studied virus in this regard, namely the tomato yellow leaf curl virus (TYLCV) and its closely related isolates. Additionally, the review aims at drawing attention to the recent knowhow of unorthodox virus-B. tabaci interactions. The recent knowledge of whitefly-mediated transmission of two recombinant poleroviruses (Luteoviridae), a virus group with an ssRNA genome and known to be strictly transmitted with aphids, is discussed with its broader context in the emergence of new whitefly-driven virus diseases.