This chapter explores the application of the wavelet transform in denoising and compression. Denoising using wavelets employs thresholding techniques to remove noise while preserving significant signal structures. The chapter discusses wavelet-based signal compression, leveraging multiresolution decomposition to achieve efficient representation with minimal loss of information. The fundamentals of compression are introduced followed by quantization, which maps continuous values to discrete levels to optimize storage and transmission. The role of wavelets in audio compression and image compression is discussed, focusing on their ability to retain essential signal components while reducing data size. The JPEG 2000 standard is detailed, highlighting its wavelet-based approach for scalable image coding. Finally, video compression techniques utilizing wavelets are discussed.