Wavelet-based statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly Gaussian. These models are unrealistic for many real-world signals. In this paper, we develop a new framework for statistical signal processing based on wavelet-domain hidden Markov models (HMMs). The framework enables us to concisely model the statistical dependencies and non-Gaussian Statistics encountered with real-world signals. Wavelet-domain HMMs are designed with the intrinsic properties of the wavelet transform in mind and provide powerful yet tractable probabilistic signal modes. Efficient Expectation Maximization algorithms are developed for fitting the HMMs to observational signal data. The new framework is suitable for a wide range of applications, including signal estimation, detection, classification, prediction, and even synthesis. To demonstrate the utility of wavelet-domain HMMs, we develop novel algorithms for signal denoising, classificaion, and detection.