The ring of multivariate polynomials F[x_1, x_2, ..., x_n] is a unique factorization domain. We consider the following problem: ``Is there an 'efficient' algorithm that outputs a non-trivial factor of the given input polynomial''. This question has applications in algebraic complexity, for example, in proving the connection between polynomial identity testing (PIT) and lower bounds. In this talk, we will consider the closure of various classes of polynomial families under factorization. [Kaltofen86-90] studied this problem for VP. A slew of work in the recent years has brought it back into the limelight: [DSY09] studied circuits of small depth and factors of a special form, [Oliveria16] studied formulas of small depth, [DSS18] studied ABPs and formulas, [CKS18] studied the polynomial class VNP. We will take a look at these algorithms and state some open problems in the area.