Opposite to the conventional wisdom, practical considerations for out-of-band emission (OOBE) suppression and adjacent channel interference (ACI) rejection in orthogonal frequency division multiplexing (OFDM) -based cognitive radio systems are not completely alike. For example, ACI will increase after discarding the cyclic prefix (CP) because the interference signal is also truncated during the CP removal process. Furthermore, effective OOBE is much larger than the estimated OOBE if there is a timing offset (TO) between the primary and secondary users. To the best of our knowledge, these and some other practical issues have not been well addressed. Various important practical issues (including multipath delay spread, high peak-to-average power ratio (PAPR), spectral efficiency loss, high complexity, sensitivities to frequency and timing offsets, non-contiguous and dynamically changing spectrum, CP removal, spectral containment, etc.) concerning OOBE suppression and ACI rejection are studied in this paper. Numerical results show that none of the existing approaches can deal with all practical issues satisfactorily. Hybrid combinations of frequency-domain approaches (spectral precoding and PAPR precoding) and time-domain approaches (windowing and filtering) are developed to maintain the merits and mitigate the drawbacks of each constituent approach in order to deal with these practical challenges. It is shown that a combination of filtering and precoding provides the best OOBE suppression and a combination of windowing and precoding provides the best ACI rejection characteristics in our numerical examples.