This paper discusses the research issues that need to be addressed in order to create a personal distributed environment where people interact with various companion, embedded, or invisible computers not only in their close vicinity but potentially anywhere. These systems are called personal networks (PNs). They constitute a category of distributed systems with very specific characteristics. They are configured in an ad hoc fashion, as the opportunity and the demand arise, to support personal applications. PNs consist of communicating clusters of personal digital devices, devices shared with other people and even infrastructure-based systems. At the heart of a PN is a core Personal Area Network (PAN), which is physically associated with the owner of the PN. Unlike the present PANs that have a geographically limited coverage, the Personal Operating Space, PNs have an unrestricted geographical span, and incorporate devices into the personal environment regardless of their geographic location. In order to do this they need the services of infrastructure-based networks and ad-hoc networks to extend their reach. A PN extends and complements the concept of pervasive computing. We show that PNs introduce new design challenges due to the heterogeneity of the involved technologies, the need for self-organization, the dynamics of the system composition, the application-driven nature, the co-operation with infrastructure-based networks, and the security hazards. We discuss the impact of these problems on network design, assess present and proposed solutions, and identify the research issues.