In 1978, a significant breakthrough was achieved in the study of percolation theory: Russo and independently Seymour and Welsh proved general bounds on crossing probabilities for Bernoulli percolation in the plane. This result, commonly known as the Russo-Seymour-Welsh (RSW) theorem, swiftly became a cornerstone in the analysis of critical Bernoulli percolation. For example, it played a pivotal role in Kesten’s proof that \(p_c=1/2\) for bond percolation on \(\mathbb {Z}^2\) and in Smirnov’s proof demonstrating the conformal invariance of critical site percolation on the triangular lattice. Recently, the theory has been extended to large classes of percolation models, leading to major breakthroughs in the study of critical phenomena for percolation, spin systems, and random height functions. In this chapter, we introduce the RSW theory in the simple setup of Bernoulli percolation. We present some classical applications and give two proofs of the RSW theorem in this framework: the first one is a variant of the original argument, while the second proof is based on recent progress in generalizing the theory.