Learning is a predominant theme for any intelligent system, humans, or machines. Moving beyond the classical paradigm of learning from past experience, e.g., offline supervised learning from given labels, a learner needs to actively collect exploratory feedback to learn from the unknowns, i.e., learning through exploration. This tutorial will introduce the learning by exploration paradigm, which is the key ingredient in many interactive online learning problems, including the multi-armed bandit and, more generally, reinforcement learning problems. In this tutorial, we will first motivate the need for exploration in machine learning algorithms and highlight its importance in many real-world problems where online sequential decision making is involved. In real-world application scenarios, considerable challenges arise in such a learning problem, including sample complexity, costly and even outdated feedback, and ethical considerations of exploration (such as fairness and privacy). We will introduce several classical exploration strategies and then highlight the aforementioned three fundamental challenges in the learning from exploration paradigm and introduce the recent research development on addressing them, respectively.