Begomoviruses are the most prevalent plant-infecting virus genus, identified by a circular single-stranded DNA genome. The proteins encoded by these viruses are multifunctional and effectively modulate the host's cellular response during infection. Begomovirus-host interactions alter host gene expression patterns, redirect signaling pathways, disturb protein degradation pathways, and reprogram cellular metabolism to establish a successful infection. This review summarises known studies about the genome organisation of begomoviruses and altered cellular processes during infection at a molecular level. In addition, we emphasise proteins involved in intercellular trafficking of the viral genome for systemic infection and counteracting host small interfering RNA silencing and discuss different approaches for virus management based on the virus’s offensive and the host’s defensive strategies.