While experimental evolution has been vital for understanding the phenotypic and genomic dynamics of adapting populations, experiments are often done in the context of just one environmental stressor at a time. Natural populations, however, typically experience complex environments in which multiple stressors are acting simultaneously. Interactions between stressors are well-known phenomena, but how such interactions affect the genetic basis of adaptation is poorly understood. In particular, adaptation to one stressor may affect interactions with other stressors, fundamentally changing the adaptive landscape and course of evolution. Here we describe the dynamics of rapid adaptation to increasingly complex environments in populations of the yeast Saccharomyces cerevisiae. Initially isogenic populations of yeast were exposed to full factorial combinations of four stressors (salt, low glucose, antifungal, and high heat) for approximately 100 generations. We observed rapid fitness increases in complex environments, mediated by the evolution of trade-offs and interactions between the individual stressors of the complex environments. By combining time-series phenotypic and pool-seq genomic data, we determined: 1) if the fitness effects of simple environments are predictive of combined stressor effects on fitness; 2) if the genetic architecture of adaptation to simple environments is predictive of the genetic architecture of adaptation to complex environments; 3) if adaptation to multiple stressors occurs concurrently or sequentially; and 4) if the order of adaptation or the evolution of trade-offs depends on the genetic architecture of adaptation to the underlying stressors.