Abstract: Let K be an algebraically closed field of arbitrary characteristic. Given three elements of some Lie algebra over K, we say that these elements form an sl_2 triple if they generate a subalgebra which is a homomorphic image of sl_2. In this talk I will introduce Lie algebras and sl_2-triples before discussing the Jacobson-Morozov theorem in characteristic 0, and the progress made in extending this result to fields of characteristic p. In particular, I will focus on the results in classical Lie algebras, which can be found as subsets of gl_n(K).