Interval graphs and interval orders are two classes of discrete structures that arise naturally in many real-world problems. They find applications in scheduling, archaeology, genetics, psychology, and circuit design, among others. In this talk, we will give a short introduction to the theory of interval graphs and orders. In particular, we will discuss the connection between these two types of structures, how they can be characterized, and why they are important from both a theoretical and a practical point of view. We will conclude by mentioning some special cases and generalizations.