Wavelet transforms have proven to be useful tools for several applications, including signal analysis, signal compression and numerical analysis. This paper surveys the VLSI architectures that have been proposed for computing the Discrete and Continuous Wavelet Transforms for 1-D and 2-D signals. The architectures are based upon on-line versions of the wavelet transform algorithms. These architectures support single chip implementations and are optimal with respect to both area and time under the word-serial model.