The wavelet transform has a powerful time-frequency analysis and signal-coding tool suitable for use in the manipulation of complex nonstationary signals. This article provides an overview of the emerging role of wavelet-transform analysis in biomedical signal processing and analysis. It also provides a brief overview of the theory of the transform in its two distinct and very different forms: continuous and discrete. In conclusion, it has been shown that the wavelet transform is a flexible time-frequency decomposition tool that can form the basis of useful signal analysis, and coding schemes. It is envisaged that the future will see further application of the wavelet transform to biomedical signal analysis, as the emerging technologies based on them are honed for practical purposes.