Modern wireless communication systems require high transmission rates, giving rise to frequency selectivity due to multipath propagation. In addition, high-mobility terminals and scatterers induce Doppler shifts that introduce time selectivity. Therefore, advanced techniques are needed to accurately model the time- and frequency-selective (i.e., doubly selective) channels and to counteract the related performance degradation. In this paper, we develop new receivers for orthogonal frequency-division multiplexing (OFDM) systems and single-carrier (SC) systems in doubly selective channels by embedding the channel estimation task within low-complexity block turbo equalizers. Linear minimum mean-squared error (MMSE) pilot-assisted channel estimators are presented, and the soft data estimates from the turbo equalizers are used to improve the quality of the channel estimates.