Comparative genomics and systems biology offer unprecedented opportunities for testing central tenets of evolutionary biology formulated by Darwin in the Origin of Species in 1859 and expanded in the Modern Synthesis 100 years later. Evolutionary-genomic studies show that natural selection is only one of the forces that shape genome evolution and is not quantitatively dominant, whereas non-adaptive processes are much more prominent than previously suspected. Major contributions of horizontal gene transfer and diverse selfish genetic elements to genome evolution undermine the Tree of Life concept. An adequate depiction of evolution requires the more complex concept of a network or 'forest' of life. There is no consistent tendency of evolution towards increased genomic complexity, and when complexity increases, this appears to be a non-adaptive consequence of evolution under weak purifying selection rather than an adaptation. Several universals of genome evolution were discovered including the invariant distributions of evolutionary rates among orthologous genes from diverse genomes and of paralogous gene family sizes, and the negative correlation between gene expression level and sequence evolution rate. Simple, non-adaptive models of evolution explain some of these universals, suggesting that a new synthesis of evolutionary biology might become feasible in a not so remote future.