Adaptive radiation is defined as the evolution of ecological and phenotypic diversity within a rapidly multiplying lineage. When it occurs, adaptive radiation typically follows the colonization of a new environment or the establishment of a “key innovation,” which opens new ecological niches and/or new paths for evolution. Here, we take advantage of recent developments in speciation theory and modern computing power to build and explore a large-scale, stochastic, spatially explicit, individual-based model of adaptive radiation driven by adaptation to multidimensional ecological niches. We are able to model evolutionary dynamics of populations with hundreds of thousands of sexual diploid individuals over a time span of 100,000 generations assuming realistic mutation rates and allowing for genetic variation in a large number of both selected and neutral loci. Our results provide theoretical support and explanation for a number of empirical patterns including “area effect,” “overshooting effect,” and “least action effect,” as well as for the idea of a “porous genome.” Our findings suggest that the genetic architecture of traits involved in the most spectacular radiations might be rather simple. We show that a great majority of speciation events are concentrated early in the phylogeny. Our results emphasize the importance of ecological opportunity and genetic constraints in controlling the dynamics of adaptive radiation.