Molecular dynamics simulations are used to study the equilibrium properties and collapse dynamics of a heteropolymer in the presence of an explicit solvent in two dimensions. The system consists of a single copolymer chain composed of hydrophobic (H) and hydrophilic (P) monomers, immersed in a Lennard-Jones solvent. We consider HP chains of varying hydrophobic number fraction nH, defined as the ratio of the number of H monomers to the total number of monomers. We also consider homopolymer chains with a uniform variable degree of hydrophobicity λ, which describes the hydrophobic-solvent interaction, and which ranges from hydrophilic (λ=0) to hydrophobic (λ=1). We investigate the effects of varying nH and λ, the HP sequencing, and the solvent density on the equilibrium and collapse properties of the chain. For sufficiently high nH, we observe a collapse transition for random copolymers from a stretched coil to a liquidlike globule upon a decrease in temperature; the transition temperature decreases with increasing nH. The transition can also be induced at a fixed (and sufficiently low) temperature by varying nH for random copolymers or λ for homopolymers. We find that polymer size varies inversely with solvent density. The rate of polymer collapse is found to strongly vary inversely with increasing nH and λ for copolymers and homopolymers, respectively. Further, the collapse rates for these two cases are very close for nH=λ, except at lower values (nH=λ≈0.5), where the homopolymers collapse more rapidly. At moderate densities (ρ=0.5–0.7, in LJ reduced units), we find that random copolymers collapse more rapidly at low density and that this difference tends to increase with decreasing nH. At fixed solvent density and nH we find the collapse rate differs little for random copolymers, and multi-block copolymers with equal nH. Finally, the simulations suggest that copolymers tend to collapse by a uniform thickening rather than by first forming locally collapsed clusters which aggregate at longer time. The exception to this appears to be block-copolymers comprised of sufficiently long alternating H and P blocks.