Viral diseases transmitted by insects to plants cause severe agricultural damage and arboviruses transmitted to humans cause severe disease outbreaks. The interaction between viruses and the insect defences is complex and has evolved into acting-counteracting molecular interplays. Viruses depict complex molecular mechanisms to ensure invasion, replication and exit the insect host cell, to invade other cells. On the other hand, insect cells use molecular strategies to recognize, halt replication and eliminate the invaders. In turn, virus counteract with evasive strategies. The main antiviral defence mechanism RNA interference (RNAi) recognizes and degrades viral RNA, thereby inhibiting viral replication. These in conjunction with other canonical immune pathways, Toll, IMD, JAK/STAT and Akt-ERK developed mainly to combat bacteria, fungi and protozoa, along with mechanisms to eliminate infected cells like apoptosis and phagocytosis comprise a multifactorial system. Insects exposed to an attenuated or sublethal viral infection could respond with faster and enhanced immune responses to the same pathogen (priming), which is like immunological memory in vertebrates. Several mechanisms have been proposed to explain priming, including endoreplication, epigenetic gene modifications by DNA methylation and histone acetylation. Priming could be inherited by the offspring (transgenerational immune priming, TGIP). However, the precise molecular mechanisms underlying TGIP remain to be elucidated. This article reviews the molecular mechanisms employed by insects to combat viral infections, discusses the current information and the outstanding research questions in the area.