Establishing applications based on the popular peer-to-peer (P2P) paradigm in mobile ad hoc networks (MANET) requires the employment of efficient mechanisms for communication and information exchange among peers. In this paper, we show that P2P systems designed for the wireline Internet cannot be deployed in MANET in a straightforward way. As a major shortcoming, these systems construct an overlay network consisting of application-layer connections that do not reflect the network-layer topology of the MANET. Furthermore, overlay construction and maintenance does not consider node mobility. We present two solutions to cope with these shortcomings: P2P communication based on cross-layer cooperation and P2P information exchange by epidemic dissemination. As an example for a system that implements the first concept, we describe the Optimized Routing Independent Overlay Network (ORION). As an example for a system that implements the second concept, we describe Passive Distributed Indexing (PDI). Detailed simulation studies show that both ORION and PDI provide efficient building blocks for the deployment of P2P computing applications in MANET.