Orthogonal frequency division multiplexing (OFDM) in next generation wireless systems provides high downlink data rates by employing frequency-domain scheduling and rate adaptation at the base station (BS). However, in order to control the significant feedback overhead required by these techniques, feedback reduction schemes are essential. Best-m feedback is one such scheme that is implemented in OFDM standards such as Long Term Evolution. In it, the sub channel (SC) power gains of only the m strongest SCs and their corresponding indices are fed back to the BS. However, two assumptions pervade most of the literature that analyze best-m feedback in OFDM systems. The first one is that the SC gains are uncorrelated. In practice, however, the SC gains are highly correlated, even for dispersive multipath channels. The second assumption deals with the treatment of unreported SCs, which are not fed back by the best-m scheme. If no user reports an SC, then no data transmission is assumed to occur. In this thesis, we eschew these assumptions and investigate best-m feedback in OFDM systems with correlated SC gains. We, first, characterize the average throughput as a function of correlation and m. A uniform correlation model is assumed, i.e., the SC gains are correlated with each other by the same correlation coefficient. The system model incorporates greedy, modified proportional- fair, and round robin schedulers, discrete rate adaptation, and non-identically distributed SC gains of different users. We, then, generalize the model to account for feedback delay. We show in all these cases that correlation degrades the average throughput. We also show that this effect does not arise when users report all the SC power gains to the BS. In order to mitigate the reduction in the average throughput caused by unreported SCs, we derive a novel, constrained minimum mean square error channel estimator for the best-m scheme to estimate the gains of these unreported SCs. The estimator makes use of the additional information, which is unique to the best-m scheme, that the estimated SC power gains must be less than those that were reported. We, then, study its implications on the downlink average cell throughput, again for different schedulers. We show that our approach reduces the root mean square error and increases the average throughput compared to several approaches pursued in the literature. The more correlated the SC gains, greater is the improvement.