Given the ever-growing demand for radio spectrum, cognitive radio has recently emerged as an attractive wireless communication technology. This dissertation is concerned with developing spectrum sensing algorithms in cognitive radio networks where a single or multiple cognitive radios (CRs) assist in detecting licensed primary bands employed by single or multiple primary users. First, given that orthogonal frequency-division multiplexing (OFDM) is an important wideband transmission technique, detection of OFDM signals in low-signal-to-noise-ratio scenario is studied. It is shown that the cyclic prefix correlation coefficient (CPCC)-based spectrum sensing algorithm, which was previously introduced as a simple and computationally efficient spectrum-sensing method for OFDM signals, is a special case of the constrained generalized likelihood ratio test (GLRT) in the absence of multipath. The performance of the CPCC-based algorithm degrades in a multipath scenario. However when OFDM is implemented, by employing the inherent structure of OFDM signals and exploiting multipath correlation in the GLRT algorithm a simple and low-complexity algorithm called the multipath-based constrained-GLRT (MP-based C-GLRT) algorithm is obtained. Further performance improvement is achieved by combining both the CPCC- and MP-based C-GLRT algorithms. A simple GLRT-based detection algorithm is also developed for unsynchronized OFDM signals. In the next part of the dissertation, a cognitive radio network model with multiple CRs is considered in order to investigate the benefit of collaboration and diversity in improving the overall sensing performance. Specially, the problem of decision fusion for cooperative spectrum sensing is studied when fading channels are present between the CRs and the fusion center (FC). Noncoherent transmission schemes with on-off keying (OOK) and binary frequency-shift keying (BFSK) are employed to transmit the binary decisions to the FC. The aim is to maximize the achievable secondary throughput of the CR network. Finally, in order to reduce the required transmission bandwidth in the reporting phase of the CRs in a cooperative sensing scheme, the last part of the dissertation examines nonorthogonal transmission of local decisions by means of on-off keying. Proposed and analyzed is a novel decoding-based fusion rule for combining the hard decisions in a linear manner.