In this talk I will try to give some idea of what originally got me interested in the theory of noncommutative rings. The Weyl algebras are fundamental examples in noncommutative ring theory. They have many interesting properties which illustrate the many ways that noncommutative rings are more complicated (and intriguing) than commutative ones. After introducing these examples, I will discuss how Weyl algebras have served as a starting point for one avenue in my recent research.