This dissertation aims to apply and extend structural economic methods to contexts where agents' choices may be influenced by idiosyncratic behavioral factors. Such generalizations enable us to explain empirical economic puzzles and to better predict the effects of different policies. Chapter 1, "Illegal Drug Use and Government Policy: Evidence from a Darknet Marketplace," joint with Priyanka Goonetilleke, Anastasia Karpova, and Peter Meylakhs, studies consumption of illegal drugs. These products are highly different from the ones traditionally studied in economics, with complex patterns in how drug users consume different illegal substances. This chapter develops a structural model of demand for illegal drug varieties and studies how consumers substitute between different types of drugs in response to government policies. Our estimation procedure exploits a novel set of micro-level moment conditions to identify correlations in preferences for specific drug types and the degree of attachment to them. The estimated model is used to evaluate counterfactual drug policies. In particular, we find that policies increasing availability of cannabis have the potential of decreasing the use of riskier drugs. However, they can also cause a sharp increase in cannabis use. Chapter 2, "Hydra: Lessons from the World’s Largest Darknet Market," joint with Priyanka Goone-tilleke and Alex Knorre, complements the discussion of drug consumption by providing a comprehensive description of Hydra, the darknet marketplace that was the origin of data used to estimate the model in Chapter 1. We quantitatively examine the scale and the structure of the marketplace using data scraped from the platform. The phenomenon of Hydra suggests that shut-down policies applied to darknet marketplaces have a large effect and implicitly shape the whole drug market. Without these policies, a pervasive digitalization of drug trade can occur. Chapter 3, "An Economy of Neural Networks: Learning from Heterogeneous Experiences," studies behavior of economic agents who might be imperfectly rational because deriving the optimal decision rule is computationally hard or because they might have limited information about the environment in which they make decisions. It develops a dynamic model of bounded rationality, relying on ideas from deep reinforcement learning. In the model, agents improve their decision rules over time, guided by the utility flow they derived from past decisions. The approach I develop can be used to relax the assumption of rational expectations in a large set of DSGE models. I apply it to the canonical framework of Aiyagari (1994), in which consumers make saving decisions when their income is subject to idiosyncratic fluctuations. The model enables me to explain several empirical puzzles, in particular, the high share of the population with no savings.