Surfaces, with their highly constrained topology and geometry, provide a surprisingly effective means for probing the rich world of 3-manifolds. We give a gentle introduction to the Thurston norm on the second homology of a 3-manifold, which measures the topological complexity of a "simplest" surface representing a given class. This measure proves to be a highly useful tool toward studying a manifold; to wit, we explain how some of the biggest results in modern 3-manifold topology can be understood as answering basic questions about the Thurston norm.