Accurate timing is critical in many industries, from time-stamping grocery receipts to facilitating stock-market transactions and supporting precise navigation, localization, and guidance. High levels of precision are currently achieved using physically large, power-hungry atomic clocks that rely on energy-level transitions in a chosen atomic species. Recently, commercially available chip-scale atomic clocks (CSACs) have emerged, offering atomically precise timing in a compact, low-power package that can be operated on a battery for extended periods. Such clocks have important applications in underwater timing for oil and gas exploration, enhanced GPS receivers, and are being adopted for application to the energy grid, where large clocks are impractical. These devices contain a microwave local oscillator (LO) that generates the RF used to interrogate the atoms and, once locked to the atomic resonance, serves as the clock output. This article reviews the state of the art in microwave CSACs, with a focus on the engineering requirements for compact, low-power microwave LOs used to lock to the atomic transition. Several different LO designs are surveyed and compared in terms of power consumption, phase noise, and suitability for use in miniaturized clocks. The frequency control electronics needed to operate CSACs are also discussed. Finally, potential future improvements to all clock electronics for CSACs are highlighted.