19th century biologists believed that the environment generates heritable variation, but the 20th century Modern Synthesis limited the environment’s evolutionary role to selecting among randomly occurring genetic variants. However, diverse lines of evidence suggest that both environmental and stochastic variation in phenotype can be transmitted nongenetically to descendants, and could play important roles in many evolutionary contexts. This evidence suggests a need to broaden the concept of heredity to incorporate both genetic and nongenetic mechanisms of inheritance, and to incorporate both forms of inheritance in evolutionary theory. I will outline recent steps towards such a model of evolution. I will also discuss the more radical (and problematic) idea that nongenetic inheritance and other developmental processes can enable adaptive evolution without natural selection.