DNA viruses promote cell cycle progression, stimulate unscheduled DNA synthesis, and present the cell with an extraordinary amount of exogenous DNA. These insults elicit vigorous responses mediated by cellular factors that govern cellular homeostasis. To ensure productive infection, adenovirus has developed means to inactivate these intracellular antiviral responses. Among the challenges to the host cell is the viral DNA genome, which is viewed as DNA damage and elicits a cellular response to inhibit replication. Adenovirus therefore encodes proteins that dismantle the cellular DNA damage machinery. Studying virus-host interactions has yielded insights into the molecular functioning of fundamental cellular mechanisms. In addition, it has suggested ways that viral cytotoxicity can be exploited to offer a selective means of restricted growth in tumor cells as a therapy against cancer. In this review, we discuss aspects of the intracellular response that are unique to adenovirus infection and how adenoviral proteins produced from the early region E4 act to neutralize antiviral defenses, with a particular focus on DNA damage signaling.