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Interference plays a crucial role for performance degradation in communication networks nowadays. An appealing approach to interference avoidance is the Interference Cancellation (IC) methodology. Particularly, the Successive IC (SIC) method represents the most effective IC-based reception technique in terms of Bit-Error-Rate (BER) performance and, thus, yielding to the overall system robustness. Moreover, SIC in conjunction with Orthogonal Frequency Division Multiplexing (OFDM), in the context of SIC-OFDM, is shown to approach the Shannon capacity when single-antenna infrastructures are applied while this capacity limit can be further extended with the aid of multiple antennas. Recently, SIC-based reception has studied for Orthogonal Frequency and Code Division Multiplexing or (spread-OFDM systems), namely OFCDM. Such systems provide extremely high error resilience and robustness, especially in multi-user environments. In this paper, we present a comprehensive survey on the performance of SIC for single- and multiple-antenna OFDM and spread OFDM (OFCDM) systems. Thereby, we focus on all the possible OFDM formats that have been developed so far. We study the performance of SIC by examining closely two major aspects, namely the BER performance and the computational complexity of the reception process, thus striving for the provision and optimization of SIC. Our main objective is to point out the state-of-the-art on research activity for SIC-OF(C)DM systems, applied on a variety of well-known network implementations, such as cellular, ad hoc and infrastructure-based platforms. Furthermore, we introduce a Performance-Complexity Tradeoff (PCT) in order to indicate the contribution of the approaches studied in this paper. Finally, we provide analytical performance comparison tables regarding to the surveyed techniques with respect to the PCT level.