The high time resolution of ultra-wide-band (UWB) signals facilitates very precise position estimation in indoor scenarios. This paper reviews the problem of position estimation in UWB systems, beginning with an overview of the characteristics of the UWB positioning system. This overview is followed by the fundamentals of positioning. Two key challenges are issued which are the problem of UWB signal sampling and the problem of TOA estimation. Compressive Sensing theory is applied to solve these problems and research results are given. Finally, a real-time precise location system for business is described.