In one of his few major oversights, Darwin failed to appreciate that male-male competition and sexual selection can continue even after copulation has begun. The postcopulatory equivalents of both direct male-male battles (sperm competition) and female choice (cryptic female choice) occur within the female's body. Recognition of this hidden, but intense, sexual competition provides new insights into a variety of fields. These include the hyperdiverse and paradoxically elaborate morphology of both sperm and male genitalia, the equally puzzling and elaborate morphology of nongenitalic male structures that are specialized to grasp and stimulate females, powerful manipulative effects of substances in male semen on female reproductive physiology, paradoxical male courtship behavior that occurs after copulation has already begun, variability in parental investments, and the puzzlingly complex and diverse interactions between sperm and female products that surround animal eggs and between male gametophytes and female tissues in flowering plants. Many bizarre traits are involved, including male genitalia that are designed to explode or fall apart during copulation leaving behind parts within the female, male genitalia that "sing" during copulation, potent seminal products that invade the female's body cavity and her nervous system to influence her behavior, and a virtual Kama Sutra of courtship behavior performed after rather than before genital coupling, including male-female dialogues during copulation.