1.1 Adaptive Filtering Review There are a number of possible degradations that can be found in a speech recording and that can affect its quality. On one hand, the signal arriving the microphone usually incorporates multiple sources: the desired signal plus other unwanted signals generally termed as noise. On the other hand, there are different sources of distortion that can reduce the clarity of the desired signal: amplitude distortion caused by the electronics; frequency distortion caused by either the electronics or the acoustic environment; and time-domain distortion due to reflection and reverberation in the acoustic environment. Adaptive filters have traditionally found a field of application in noise and reverberation reduction, thanks to their ability to cope with changes in the signals or the sound propagation conditions in the room where the recording takes place. This chapter is an advanced tutorial about multichannel adaptive filtering techniques suitable for speech enhancement in multiple input multiple output (MIMO) very long impulse responses. Single channel adaptive filtering can be seen as a particular case of the more complex and general multichannel adaptive filtering. The different adaptive filtering techniques are presented in a common foundation. Figure 1 shows an example of the most general MIMO acoustical scenario.