In this paper, the problem of optimum data detection in OFDM under severe phase noise (PHN) is addressed. Since direct maximization of the likelihood function is infeasible, the expectation-maximization (EM) algorithm is invoked as an iterative, feasible method of data detection. Two algorithms are proposed, one derived by direct application of the standard EM algorithm in the present context of OFDM data detection, whereas the other employs soft data estimates resulting in enhanced performance. The use of Kalman filtering is also examined as a means of complexity reduction and handling of the case of a non-negligible frequency offset (FO). The performance of the proposed algorithms is evaluated by simulations which show significant gains over the PHN-compensation method employed by OFDM-based standards.