Accurate positioning systems can be realized via ultra-wideband signals due to their high time resolution. In this article, position estimation is studied for UWB systems. After a brief introduction to UWB signals and their positioning applications, two-step positioning systems are investigated from a UWB perspective. It is observed that time-based positioning is well suited for UWB systems. Then time-based UWB ranging is studied in detail, and the main challenges, theoretical limits, and range estimation algorithms are presented. Performance of some practical time-based ranging algorithms is investigated and compared against the maximum likelihood estimator and the theoretical limits. The trade-off between complexity and accuracy is observed.