Since the Modern Synthesis, our ideas of evolution have mostly centered on the information encoded in the DNA molecule and their mechanisms of heredity. Increasing evidence, however, suggests that epigenetic mechanisms have the potential to perpetuate gene activity states in the context of the same DNA sequence. Here, we discuss recent compelling evidence showing that epigenetic signals triggered by environmental stress can persist over very long timeframes, contributing to phenotypic changes in relevant traits upon which selection could act. We argue that epigenetic inheritance plays an important role in fast phenotypic adaptation to fluctuating environments, ensuring the survival of the organisms of a population under environmental stress in the short term while maintaining a "bet-hedging" strategy of reverting to the original state if the environment returns to standard conditions. These examples call for a reevaluation of the role of nongenetic information in adaptive evolution, raising questions about its broader relevance in nature.