Local representations of the international time scale, Coordinated Universal Time (UTC), are maintained by approximately 69 national measurement institutes and other time laboratories. These laboratories contribute their clock and time transfer measurements for use in the computation of UTC. Although local representations of UTC, commonly called UTC(k) time scales, vary considerably, for example in the numbers of atomic clocks available, they also share many characteristics. In this paper, we examine the rationale and requirements for maintaining a local representation of UTC. Its applications might range from underpinning the reference time scale of a Global Navigation Satellite System to providing traceability for frequency and time dissemination services. We address the practical aspects of setting up and operating a UTC(k) time scale, including the equipment and algorithms that generate the time scale, optimize its performance and measure its offset from the similar time scales maintained by other laboratories. We conclude by considering briefly some future developments that may have an impact on the laboratories operating local representations of UTC.