The host invariably responds to infecting viruses by activating its innate immune system and mounting virus-specific humoral and cellular immune responses. These responses are aimed at controlling viral replication and eliminating the infecting virus from the host. However, viruses have evolved numerous strategies to counter and evade host's antiviral responses. Providing specific examples from the published literature, we discuss in this review article various strategies that viruses have developed to evade antiviral cellular responses of the host. Unraveling these viral strategies allows a better understanding of the host-pathogen interactions and their coevolution. This knowledge is important for identifying novel molecular targets for developing antiviral reagents. Finally, it may also help devise new knowledge-based strategies for developing antiviral vaccines.