Cognitive radios are the radios which use spectrum licensed to other users. For this, they perform Radio Environment Analysis, identify the Spectral holes and then operate in those holes. We consider the problem of Spectrum Sensing in Cognitive Radio Networks. Our Algorithms are based on Sequential Change Detection techniques. In this work we have used DualCUSUM, a distributed algorithm developed recently for cooperative spectrum sensing. This is used by cognitive (secondary) nodes to sense the spectrum which then send their local decisions to a fusion center. The fusion center again sequentially processes the received information to arrive at the final decision. We show that DualCUSUM performs better than all other existing spectrum sensing algorithms. We present a generalized analysis of DualCUSUM and compare the analysis with simulations to show its accuracy. DualCUSUM requires the knowledge of the channel gains for each of the secondary users and the receiver noise power. In Cognitive Radio setup it is not realistic to assume that each secondary user will have this knowledge. So later we modify DualCUSUM to develop GLRCUSUM algorithms which can work with imprecise estimates of the channel gains and receiver noise power. We show that the SNR wall problem encountered in this scenario by other detectors is not experienced by our algorithm. We also analyze the GLRCUSUM algorithms theoretically. We also apply our algorithms for detecting the presence of the primary in an Orthogonal Frequency Division Multiplexing (OFDM) setup. We first consider the Cyclic Prefix (CP) detector, which is considered to be robust to uncertainties in noise power, and further modify the CPdetector to take care of some of the common impairments like Timing offset, Frequency offset and IQ imbalance. We further modify the CPdetector to work under frequency selective channel. We also consider the energy detector under different impairments and show that the sequential detection based energy detectors outperform cyclic prefix based Detectors.