Many experimental and statistical paradigms collect and analyze behavioral data under steady-state assumptions. Such paradigms may have low external validity, since real-world decisions are often made in situations when people are still learning and adapting, or their beliefs and preferences are in a state of flux, or where the decision environment is constantly changing. I focus on experimental and real-world paradigms that represent some form of adaptive behavior. Under such situations, factoring in structural adaptivity into cognitive modeling frameworks can improve their descriptive and predictive performance, and allow us to make superior inferences about the underlying latent cognitive processes. Towards this endeavor, first, a novel probabilistic framework is proposed for representation of heuristic strategies of information search and multi-attribute choice within a model of learning. Second, a novel adaptive reference point mechanism is introduced, and I show how this can be used in a variety of different tasks and applications, and be incorporated into cognitive frameworks to structurally capture the adaptive process. This mechanism provides superior predictive performance along with psychologically meaningful parameter inference in tasks ranging from signal detection, bandit problems, judgments about estimating true values, consumption behavior, probability tracking, and expectation formation. Third, I show how cognitive modeling can be applied to adaptive population behavior in the real world. Real world data is used to make inferences about the latent processes involved in aspects such as the changing nature of cycles of violence, and the impact of tax policies on changing consumption patterns. Incorporating cognitive modeling frameworks and psychological insights to constrain econometric models yields possibly simpler models, but with directly interpretable parameter inferences. Fourth, cognitive modeling approaches are used to design choice architecture frames to create behavioral nudges within a risk allocation paradigm, where people change their behavior based on representational, rather than meaningful changes in their environment.