This paper addresses the issue of iterative space-time equalization for multiple-input-multiple-output (MIMO) frequency-selective fading channels. A new soft equalization concept based on successive interference cancellation (SIC) is introduced for a space-time bit-interleaved coded modulation (STBICM) transmission. The proposed equalizer allows us to separate intersymbol interference (ISI) and multiantenna interference (MAI) functions. Soft ISI is successively suppressed using a low-complexity suboptimum minimum mean square error (MMSE) criterion. The decoupling of ISI and MAI offers more flexibility in the design of the whole space-time equalizer. Different multiantenna detection criteria can be considered, ranging from simple detectors to the optimal maximum aposteriori (MAP) criterion. In particular, we introduce two soft equalizers, which are called SIC/SIC and SIC/MAP, and we show that they can provide a good performance-to-complexity tradeoff for many system configurations, as compared with other turbo equalization schemes. This paper also introduces an MMSE-based iterative channel state information (CSI) estimation algorithm and shows that attractive performance can be achieved when the proposed soft SIC space-time equalizer iterates with the MMSE-based CSI estimator.