This paper represents a first step in exploring the formation of connected topologies in ad-hoc networks built on the Bluetooth technology. Connectivity is the most basic requirement for any system aimed at allowing devices to communicate with each other and in this paper we illustrate that this seemingly innocuous goal gives rise to many significant challenges in the context of the Bluetooth technology. We start with a brief overview of Bluetooth and its operation and then identify some of the major problems the technology faces when used to build ad-hoc networks. The paper's contributions are in introducing basic algorithmic problems associated with building connected Bluetooth networks and in developing several possible solutions capable of generating "good" connected topologies.