Patent thickets, layers of licenses a firm needs to be able to offer products that embody technologies owned by multiple firms, and licensing policies have drawn increasing scrutiny from policy makers. Patent thickets involve complementary products, which gives rise to double marginalization -- the so-called royalty stacking problem -- and has the potential to retard diffusion of new technologies and reduce consumer welfare. This paper examines the impact of licensing policies of one or more upstream owners essential} intellectual property (IP) on the downstream firms that require access to that IP. The terms under which downstream firms can access this IP affects entry decisions, product diversity, prices and welfare. We consider both the case in which a single party controls the essential IP and the case in which different parties control complementary pieces of essential IP. We compare the outcome of several alternative standard licensing arrangements, such as flat rate access fees, royalty percentages, per unit fees, patent pools and cross-licensing arrangements, with or without vertical integration. We first consider the case where there is a single upstream owner of essential IP. Increasing the number of licenses enhances product variety, which creates added value, but it also intensifies downstream competition, which dissipates profits. We derive conditions under which the upstream IP monopoly will then want to provide an excessive or insufficient number of licenses, relative to the number that maximizes consumer surplus or social welfare. When there are multiple owners of essential IP, royalty stacking can reduce the number of the downstream licensees, but also the downstream equilibrium prices the consumers face. The paper derives conditions determining whether this reduction in downstream price and variety is beneficial to consumers or society. Finally, the paper explores the impact of alternative licensing policies. With fixed license fees or royalties expressed as a percentage of the price, an upstream IP owner cannot control the intensity of downstream competition. In contrast, volume-based license fees (i.e., per-unit access fees), do permit an upstream owner to control downstream competition and to replicate the outcome of complete integration. The paper also shows that vertical integration can have little impact on downstream competition and licensing terms when IP owners charge fixed or volume-based access fees.