The Hilbert scheme of n points on a smooth projective surface X is a smooth projective variety due to a classical result of Fogarty. A natural question about these spaces is to determine their ample divisors. Using techniques from derived categories developed by Bayer and Macrì, we describe the nef cones if X has Picard rank 1, irregularity 0 and n is large. Moreover, we compute the nef cone if X is the blow-up of the projective plane at 8 general points for any n. This is joint work with Bolognese, Huizenga, Lin, Riedl, Woolf, and Zhao originating from the boot camp of the 2015 Algebraic Geometry Summer Institute in Utah.