Light detection and ranging (Lidar) systems based on single-photon detection can be used to obtain range and reflectivity information from 3D scenes with high range resolution. However, reconstructing the 3D surfaces from the raw single-photon waveforms is challenging, in particular when a limited number of photons is detected and when the ratio of spurious background detection events is large. This paper reviews a set of fast detection algorithms, which can be used to assess the presence of objects/surfaces in each waveform, allowing only the histograms where the imaged surfaces are present to be further processed. The original method we recently proposed is extended here using a multiscale approach to further reduce the computational complexity of the detection process. The proposed methods are compared to state-of-the-art 3D reconstruction methods using synthetic and real single-photon data and the results illustrate their benefits for fast and robust target detection.