Rational lines on smooth cubic surfaces

This is a largely expository account about lines on smooth cubic surfaces over non-algebraically closed fields. In 1949, Segre proved that the number of lines on a smooth cubic surface over any field is 0, 1, 2, 3, 5, 7, 9, 15, or 27. We recall Segre's proof and give an alternate proof of this result. We then show that each of these possible line counts is realized by some smooth cubic surface when the base field is a finitely generated field of characteristic 0, a finite transcendental extension of a characteristic 0 field, or a finite field of characteristic 2 and order at least 4.