The high time resolution of ultra-wideband (UWB) signals results in a large number of multipath components (MPCs) arriving at the receiver, which presents a source of diversity. In addition to this multipath diversity, there is also repetition diversity inherent in impulse radio (IR) UWB systems, since a number of pulses are transmitted for each information symbol. In order to make optimal use of both multipath and repetition diversity, the receiver needs to consider the optimal combination of contributions from both different frames and different MPCs. In this overview paper, the optimal linear receiver for a given user in a frequency-selective multiuser environment, which combines all the samples from the received signal according to the minimum mean square error (MMSE), criterion is studied. Due to the complexity of this optimal receiver, two suboptimal receivers with lower complexity are considered, optimal frame combining (OFC) and optimal multipath combining (OMC) receivers, which reduce computational complexity by suboptimal combining in the multipath diversity and repetition diversity domains, respectively. Finally, a two-step MMSE algorithm which reduces complexity by performing MMSE combining in two steps is presented, and its optimality properties are discussed. Simulations are performed to compare the performance of different receivers.