Polymer "brushes" are formed when long-chain molecules are somehow attached by one end at an interface with a relatively small area per chain. Such adsorbed brushes in the presence of solvent may be used to modify surface properties, stabilize colloidal particles, etc. Strongly segregated block copolymer phases, or interfacial layers of such "polymeric surfactants" may also be modeled in terms of "melt brushes," (i.e., brushes without solvent). In both cases, when chain attachments are crowded on the interface, the chains stretch out to avoid neighboring chains. The resulting physical state has properties markedly different from polymer solutions, gels, or weakly adsorbed polymer layers. When the chains are strongly stretched, their statistical mechanics become simpler, as fluctuations around the set of most probable conformations are suppressed. This makes possible many pencil-and-paper calculations of brush properties, including bending and compressional moduli, and detailed knowledge of the chain conformations. As a recent example, I will describe calculations of phase diagrams of strongly segregated block copolymers including bicontinuous double-diamond phases.