We discuss the basic physical principles of laser optical pumping double-resonance spectroscopy, which form the basis of state-of-the-art vapour-cell atomic frequency standards using laser optical pumping of Rb atoms. The main effects limiting the frequency stability of Rb vapour-cell atomic clocks are identified, and their impact on the development of high-performance frequency standars and their transfer from research laboratories to industry and space is discussed. As examples, the impact of the AC stark effect and the realated issue of laser frequency stabilisation are dealt with in more detail. The main features of the present state-of-the-art Rb atomic frequency standards will be illustrated using the example of the development of atomic clocks for satellite navigation and positioning systems (GPS, GLONAS, GALILEO, etc.) as well as some directions for further improvements that could overcome present day limitations. Such compact Rb clocks find their applications in, for example, telecommunications, local timekeeping and synchronisation, and space applications like satellite navigation and science missions. An overview of other, alternative clock schemes is given and critical issues for future developments towards further performance improvement or device miniaturisation in the field of vapour-cell atomic clocks are discussed.