The restricted solid-on-solid (RSOS) model is a model of continuous-time surface growth characterized by the constraint that adjacent height differences are bounded by a fixed constant. Though the model is conjectured to belong to the KPZ universality class, mathematical progress on the model is very sparse. We study basic properties of the model and establish bounds on surface height fluctuations as a function of time. A linear fluctuation bound is proven for all dimensions, and a logarithmic fluctuation lower bound is given for dimension one. The proofs rely on a new characterization of RSOS as a type of first passage percolation on a disordered lattice, which is of independent interest. The logarithmic lower bound is established by showing equality in distribution to the minimum of a certain dual RSOS process.