The evolutionary forces underlying the rapid evolution in sequences and functions of new genes remain a mystery. Adaptation by natural selection explains the evolution of some new genes. However, many new genes perform sex-biased functions that have rapidly evolved over short evolutionary time scales, suggesting that new gene evolution may often be driven by conflicting selective pressures on males and females. It is well established that such sexual conflict (SC) plays a central role in maintaining phenotypic and genetic variation within populations, but the role of SC in driving new gene evolution remains essentially unknown. This review explores the connections between SC and new gene evolution through discussions of the concept of SC, the phenotypic and genetic signatures of SC in evolving populations, and the molecular mechanisms by which SC could drive the evolution of new genes. We synthesize recent work in this area with a discussion of the case of Apollo and Artemis, two extremely young genes (<200,000 years) in Drosophila melanogaster, which offered the first empirical insights into the evolutionary process by which SC could drive the evolution of new genes. These new duplicate genes exhibit the hallmarks of sexually antagonistic selection: rapid DNA and protein sequence evolution, essential sex-specific functions in gametogenesis, and complementary sex-biased expression patterns. Importantly, Apollo is essential for male fitness but detrimental to female fitness, while Artemis is essential for female fitness but detrimental to male fitness. These sexually antagonistic fitness effects and complementary changes to expression, sequence, and function suggest that these duplicates were selected for mitigating SC, but that SC has not been fully resolved. Finally, we propose Sexual Conflict Drive as a self-driven model to interpret the rapid evolution of new genes, explain the potential for SC and sexually antagonistic selection to contribute to long-term evolution, and suggest its utility for understanding the rapid evolution of new genes in gametogenesis.