In this paper, a new class of soft-input soft-output block decision feedback equalizer (BDFE) for turbo equalization over inter-symbol interference (ISI) channels under minimum mean-square error (MMSE) criterion is proposed. First, the BDFE which employs both the a posteriori moments of estimated symbols and the a priori moments of unestimated symbols is investigated, and two recursive schemes are derived to reduce the complexity. Then, to mitigate error propagation, the bidirectional BDFE (Bi-BDFE) consisting of a forward BDFE and a backward BDFE is proposed. Furthermore, a threshold is employed to reduce the number of inverse matrix update process for the BDFE (T-BDFE), which can attain a flexible trade-off between complexity and performance. Finally, the bidirectional equalization is introduced into a low-complexity approximate solution of the BDFE (Bi-LC-BDFE) to further reduce the complexity and obtain time diversity gain, which utilizes a time-invariant covariance matrix. Simulation results show that the proposed equalizers significantly outperform the block linear equalizer (BLE), the exact MMSE-based linear equalizer (Exact-MMSE-LE) and the soft-decision feedback equalizers (SDFE), while keeping a similar complexity as the BLE. In addition, the Bi-BDFE can achieve better performance than the Max-Log-MAP equalizer while its complexity is on the same order as the BDFE.