This paper presents some of the recent challenges to the Modern Synthesis of evolutionary theory, which has dominated evolutionary thinking for the last sixty years. The focus of the paper is the challenge of soft inheritance - the idea that variations that arise during development can be inherited. There is ample evidence showing that phenotypic variations that are independent of variations in DNA sequence, and targeted DNA changes that are guided by epigenetic control systems, are important sources of hereditary variation, and hence can contribute to evolutionary changes. Furthermore, under certain conditions, the mechanisms underlying epigenetic inheritance can also lead to saltational changes that reorganize the epigenome. These discoveries are clearly incompatible with the tenets of the Modern Synthesis, which denied any significant role for Lamarckian and saltational processes. In view of the data that support soft inheritance, as well as other challenges to the Modern Synthesis, it is concluded that that synthesis no longer offers a satisfactory theoretical framework for evolutionary biology.