Abstract: Atomic clocks, surpassing a mind-boggling precision of one part in 1018, are the most accurate instruments ever made by mankind. The performance of the best clocks and other quantum sensors is limited by the quantum projection noise in the final readout measurement, a situation referred to as the standard quantum limit. Entangled states of the many-body system can be used to overcome the standard quantum limit. A particularly simple form of entanglement is spin squeezing, where the quantum noise for the variable of interest, e.g., the phase of an atomic clock, is redistributed into another variable. I will discuss how spin squeezing can be generated by coupling the atomic ensemble to an optical cavity. We report the first sizeable spin squeezing in an optical-clock atom, ytterbium, and discuss prospects for using spin squeezing to improve state-of-the-art optical-transition clocks.