Spectrum sensing is a critical function for enabling dynamic spectrum access (DSA) in a cognitive radio system. In DSA networks, unlicensed secondary users can gain access to a licensed spectrum band as long as they do not cause harmful interfere to the primary users. Although existing research has demonstrated the utility of a Markov chain for modeling the spectrum access pattern of primary users over time, little effort has been directed toward spectrum sensing based upon such models. In this thesis, we develop several sequence detection algorithms for spectrum sensing in DSA networks. We assign different costs for missed detections and false alarms and show that a suitably modified forward-backward sequence detection algorithm is optimal in minimizing the detection risk. Two advanced sequence detection algorithms, the complete forward algorithm and the complete forward partial backward algorithm are introduced. Along the way, we observe new fundamental limitations that we call the risk floor and the window length limitation of traditional physical layer detection schemes that arise from their mismatch with the primary user's channel access pattern. We also report results from preliminary experiments in which we implement and compare different detectors using a software-defined radio platform.