Cichlid fishes are famous for large, diverse and replicated adaptive radiations in the Great Lakes of East Africa. To understand the molecular mechanisms underlying cichlid phenotypic diversity, we sequenced the genomes and transcriptomes of five lineages of African cichlids: the Nile tilapia (Oreochromis niloticus), an ancestral lineage with low diversity; and four members of the East African lineage: Neolamprologus brichardi/pulcher (older radiation, Lake Tanganyika), Metriaclima zebra (recent radiation, Lake Malawi), Pundamilia nyererei (very recent radiation, Lake Victoria), and Astatotilapia burtoni (riverine species around Lake Tanganyika). We found an excess of gene duplications in the East African lineage compared to tilapia and other teleosts, an abundance of non-coding element divergence, accelerated coding sequence evolution, expression divergence associated with transposable element insertions, and regulation by novel microRNAs. In addition, we analysed sequence data from sixty individuals representing six closely related species from Lake Victoria, and show genome-wide diversifying selection on coding and regulatory variants, some of which were recruited from ancient polymorphisms. We conclude that a number of molecular mechanisms shaped East African cichlid genomes, and that amassing of standing variation during periods of relaxed purifying selection may have been important in facilitating subsequent evolutionary diversification. Genomes and transcriptomes of five distinct lineages of African cichlids, a textbook example of adaptive radiation, have been sequenced and analysed to reveal that many types of molecular changes contributed to rapid evolution, and that standing variation accumulated during periods of relaxed selection may have primed subsequent diversification. The 2,000 or so species of cichlid fish, to be found in the lakes and rivers of Africa's Rift Valley, provide the classic example of adaptive radiations. This large-scale international collaboration has sequenced and analysed the genomes and transcriptomes of five distinct lineages of African cichlids. The data reveal an excess of gene duplications in comparison to other fish species. There is an abundance of non-coding element divergence; accelerated coding sequence evolution; expression divergence associated with transposable element insertions in orthologous gene pairs; and regulation by novel miRNAs. Sequencing data from sixty individuals from six closely related Lake Victoria species point to rapid cichlid speciation associated with genome-wide diversifying selection on coding and regulatory variants, and imply that ancient periods of relaxed purifying selection enabled the accumulation of standing variation, which may have been important in facilitating diversification.