Our mobile devices regularly encounter and connect to multiple networks to maintain seamless connectivity. While this enables a variety of services we increasingly rely on, these ubiquitous network connections raise a number of important concerns. Our devices regularly send traffic over networks they do not fully trust and that are not under user control, which leads to security vulnerabilities, policies that impact performance and service availability, and privacy violations. We propose a new networking abstraction called Personal Virtual Networks, or PVNs, to address these issues. The key idea is to allow a device connecting to a foreign network to establish a virtual network under the device's full control, thus providing the illusion of a personal home network wherever the device roams. Devices can establish trusted network configurations, define policies for network traffic, and even deploy limited code that interposes on their traffic using a software middlebox environment. By making in-network resources available to devices via a secure and flexible interface, PVNs can enable more secure, private, and performant network experiences for users while potentially generating a new revenue stream for access networks that support them.