Decision makers rely on observations to make better decisions. Hence mastering the interplay between data and decision-making is a central topic to the field of OM/OR. In this dissertation, we study active learning problems (defined broadly) in the context of managing marketplaces and online platforms. Here active learning means that the data flow that the decision maker (DM) observes could be proactively and endogenously determined by the actions of the DM and possibly other agents in the environment as well. Classic dynamic learning problems typically involve resolving the tension between exploration (i.e., choosing informative actions to reduce model uncertainty) and exploitation (i.e., determining "reward maximizing" actions based on the estimated model). In Chapter 2, we consider a pure exploration problem instead, where the DM cares less about the reward flow along the way. Instead, the DM strives to take "information maximizing" actions to make high-confidence statistical inferences based on a minimal amount of data. Such pure exploration problems are very relevant in online platform operations, especially applied to survey/questionnaire design for preference learning, new product introduction, among others. Specifically, Chapter 2 studies how to individualize the menu of products shown to each consumer so that the platform only needs a minimal amount of samples to identify the consumer population's favorite product with high confidence. Chapter 3 deviates from the classic dynamic learning literature in a different dimension: it examines an environment where the data flow could be strategically manipulated by powerful agents. Specifically, in a spread betting market, the market maker (i.e., DM) wishes to learn from market transactions to move her spread lines in a way to correct mispricing. In the meanwhile, she may face an informed bettor who can profit from "flooding" the market (in the opposite direction) to exacerbate the market maker's mispricing. The goal of the DM in Chapter 3 is to design a learning algorithm that not only gathers information from the market, but also protects the DM from strategic manipulations.