Smooth cubic surfaces (over the complex numbers) contain exactly 27 lines. Degenerating them, and following where the lines go, leads to a rich theory of combinatorics. Beniamino Segre, in his book "The non-singular cubic surfaces" (1942), uses the symmetries inherent in this combinatorial framework to classify the symmetries of cubic surfaces. In this talk, we'll do some early 20th-century math and follow how Segre classifies cubic surfaces defined over the real numbers.