Heterogeneity is pervasive in social sciences and manifests in many forms across economic agents and over time. Examples include preferences for products, effects of governmental policies, capital and labor decisions by firms, investment strategies by financial agents, and a large etcetera. Economic and statistical models are by construction a stylized version of reality and group heterogeneity, if not properly accounted for, can lead to model misspecification. An important question is then whether such misspecification transmits to the economic predictions derived from those models, and what are the implications thereof. A related question is how much heterogeneity can be provably captured. This dissertation studies these two related problems—heterogeneity and misspecification—from an econometric perspective in three independent chapters. Chapter 1 treats both problems together by studying a model which allows for time-varying group-specific unobserved heterogeneity, but is misspecified such that the latent group structure cannot be accurately recovered. I show how auxiliary data can help mitigate misspecification and consistently recover time-varying group heterogeneity in an optimal way. To that end, I propose the Covariate-Assisted Shrinkage estimator, derive several analytical properties, and study its performance through simulation experiments and one empirical application. Chapters 2 and 3 zoom in on each of the aforementioned problems individually. Chapter 2 studies how much heterogeneity can be allowed while still able to guarantee valid statistical inference. The framework assumes that statistical dependence stems from links in an underlying network. The strength of dependence is left unrestricted, and conditions are given based on the network topology. Chapter 3 investigates how we should adapt our decisions in the (potential) presence of model misspecification. The starting point is a dynamically misspecified model that is used for forecasting and impulse response estimation. The results show that the consequences of model misspecification are meaningful, and using misspecification-robust methods like the proposed PC and IRFC selection criteria proves crucial.