Recently, interest has been shown in cognitive radio (CR) systems since they can op- portunistically access unused spectrum bands thereby increasing usable communication capacity. Spectrum sensing has been identified as a key function to ensure that CR can detect spectrum holes. In a CR network, a fast and accurate spectrum sensing scheme is important. Spectrum sensing can be viewed as a signal detection problem. Most of the existing spectrum sensing schemes are based on fixed sample size detectors which means that their sensing time is preset and fixed. However, the work of Wald [27] showed that a detector based on sequential detection requires less average sensing time than a fixed sample size detector. In this thesis, we have applied the method of sequential detection to reduce the average sensing time. Simulation results have shown that, compared to the fixed sample size energy detector, a sequential detector can reduce sensing time by up to 85% in the AWGN channel for the same detection performance. In order to limit sensing time, especially in a fading environment, a truncated sequential detector is developed. The simulation results show that the truncated sequential detector requires less sensing time than the sequential detector, but the performance degrades due to truncation. Finally, a cooperative spectrum sensing scheme is used where each individual sensor uses a sequential detector. The combining rule used at the fusion center is a selection combining rule. Simulation results show that the proposed cooperative spectrum sensing scheme can reduce the sensing time compared to the individual spectrum sensing scheme.