In this paper, a new approach to improving reliability and bandwidth efficiency in communications over frequencyselective channels using multiple antennas is proposed. In the heart of the new approach is a novel space-time orthogonal frequency division multiplexing (OFDM) scheme. The proposed space-time OFDM modulator translates a multiple-input multiple-output (MIMO) channel into a single-input multipleoutput (SIMO) channel without the loss of system freedom (the available diversity gain). This translation simplifies code design as compared to that in the conventional MIMO OFDM approach. Instead of more complicated space-time codes, codes that are designed for single-input fading channels can be used with the proposed space-time modulation. For bandwidth-efficient applications, a channel multiplexing scheme is developed to work with the space-time modulator. Unlike the conventional spatial multiplexing schemes, an arbitrary number of data streams can be created and each layer occupies all the transmit antennas all the time. As a result, all the available degrees of freedom are preserved for each layer and a full range of optimal tradeoffs between data rate and reliability is possible. Several examples are given to demonstrate the advantages of the proposed approach over the conventional MIMO OFDM approach.