The concept of Lyapunov exponent goes back to Lyapunov's 1892 thesis on the stability of differential equations, and has numerous applications in various branches of mathematics and science.
Starting from the 1960s, it found its proper mathematical framework in ergodic theory, where it has had a prominent role ever since. In this colloquium lecture I will review a few recent developments, especially about the way Lyapunov exponents depend on the underlying dynamical system.