We present a cross-layer modeling and design approach for multigigabit indoor wireless personal area networks (WPANs) utilizing the unlicensed millimeter (mm) wave spectrum in the 60 GHz band. Our approach accounts for the following two characteristics that sharply distinguish mm wave networking from that at lower carrier frequencies. First, mm wave links are inherently directional: directivity is required to overcome the higher path loss at smaller wavelengths, and it is feasible with compact, low-cost circuit board antenna arrays. Second, indoor mm wave links are highly susceptible to blockage because of the limited ability to diffract around obstacles such as the human body and furniture. We develop a diffraction-based model to determine network link connectivity as a function of the locations of stationary and moving obstacles. For a centralized WPAN controlled by an access point, it is shown that multihop communication, with the introduction of a small number of relay nodes, is effective in maintaining network connectivity in scenarios where single-hop communication would suffer unacceptable outages. The proposed multihop MAC protocol accounts for the fact that every link in the WPAN is highly directional, and is shown, using packet level simulations, to maintain high network utilization with low overhead.