With the rapid development of wireless communications technologies, radio spectrum has become a type of extremely scarce resources in meeting the increasing demands for broadband wireless services. However, the traditional static spectrum allocation policy leads to severe spectrum underutilization and spectrum shortage problems. The cognitive radio (CR) technology can detect the occupancy of the spectrum and enable the dynamic spectrum access (DSA) to fill the spectrum hole caused by the static allocation policy, and thus has been widely recognized as an efficient approach to solve the above problems. The distributed cognitive wireless network (CWN), which does not have central entities, is one of the major networking architectures applying the CR technology. Correspondingly, the design of DSA in distributed CWNs is crucial, yet challenging, to increasing the utilization efficiency of the wireless spectrum with dynamically-varying occupancy statuses. In this article, we present a survey on DSA protocols for distributed CWNs. In particular, we first address the challenges in the design and implementation of distributed DSA protocols. Then, we categorize the existing distributed DSA protocols based on different criteria, such as spectrum sharing modes, spectrum allocation behaviors, spectrum access modes, the usage of common control channel, spectrum usage strategies, the number of radios, and spectrum sensing techniques. We also discuss the advantages and disadvantages of each category under diverse classification criterion. Moreover, we make a comprehensive survey of the state-of-the-art distributed DSA protocols using different spectrum access modes, which can be categorized into contention-based, time-slotted, and hybrid protocols. Through the study, we find out that most of distributed DSA protocols fall into the contention-based and hybrid protocols. In addition, the ongoing standardization efforts are also reviewed. Finally, several open research issues for the distributed DSA protocols are presented, such as spectrum handoff based protocols, spectrum prediction based protocols, adaptation of the spectrum-sharing modes, protocols with cooperative spectrum sensing, as well as distributed collision avoidance mechanisms.