This paper aims at providing a tutorial introduction to adaptive filters operating in the subband or transform domain. In doing so we start off by reviewing the classical time-domain algorithms such as the {\em least mean square} algorithm (LMS) and its block oriented relative (BLMS). Following this we introduce subband domain algorithms through the block oriented discrete Fourier transform (DFT) adaptive algorithms. It is pointed out that these algorithms are essentially computationally efficient implementations of the BLMS algorithms with some possibilities for improved convergence speed. By virtue of the block oriented DFT being a particular instantiation of a critically sampled filter bank, we argue that this family of algorithms belong to the class of subband adaptive filtering algorithms. Subsequently we introduce true subband adaptive filters based on more general subband decompositions. Reasons why intuitively appealing structures based on critically sampled filter banks does not work well are given. After indicating some possible remedies for this, we present structures using orthogonal transforms for the non-subsampled signal decomposition. These algorithms lead to improved convergence when compared to the LMS algorithm, but at the expense of some additional computations. All the subband adaptive filters presented in this paper make use of the LMS algorithm in some way or another. The objective of introducing the subband decomposition is to either reduce computational complexity or to improve the speed of convergence through signal conditioning.