This paper presents an elementary proof of nonstrict Finsler's theorem and discusses five closely related theorems: Yakubovich's S-lemma, Yuan's alternative theorem, nonstrict Finsler's theorem, strict Finsler's theorem, and Finsler-Calabi's theorem. This paper discusses how one is related with another. At the end of this article we present some extensions of these results to an infinite-dimensional vector space.