One of the primary objectives of deploying cognitive radio (CR) within a dynamic spectrum access (DSA) network is to ensure that the legacy rights of incumbent licensed (primary) transmissions are protected with respect to interference mitigation when unlicensed (secondary) communications are simultaneously operating within the same spectral vicinity. In this article, we present non-contiguous orthogonal frequency division multiplexing (NC-OFDM) as a promising and practical approach for achieving spectrally agile wireless data transmission that is suitable for secondary users (SUs) to access fragmented spectral opportunities more efficiently. Furthermore, a review of the current state-of-the-art is conducted with respect to methods specifically designed to protect the transmissions of the primary users (PUs) from possible interference caused by nearby SU transceivers employing NC-OFDM. These methods focus on the suppression of out-of-band (OOB) emissions resulting from the use of NC-OFDM transmission. To achieve the required OOB suppression, we present two practical approaches that can be employed in NC-OFDM, namely, the insertion of cancellation carriers and windowing. In addition to the theoretical development and proposed improvements of these approaches the computer simulation results of their performance are presented. Several real-world scenarios regarding the coexistence of both PU and SU signals are also studied using actual wireless experiments based on software-defined radio. These simulation and experimental results indicate that OOB suppression can be achieved under real-world conditions, making NC-OFDM transmission a viable option for CR usage in DSA networks.