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Wavelets have been favorably applied in almost all aspects of digital wireless communication systems including data compression, source and channel coding, signal denoising, channel modeling and design of transceivers. The main property of wavelets in these applications is in their flexibility and ability to characterize signals accurately. In this paper recent trends and developments in the use of wavelets in wireless communications are reviewed. Major applications of wavelets in wireless channel modeling, interference mitigation, denoising, OFDM modulation, multiple access, Ultra Wideband communications, cognitive radio and wireless networks are surveyed. The confluence of information and communication technologies and the possibility of ubiquitous connectivity have posed a challenge to developing technologies and architectures capable of handling large volumes of data under severe resource constraints such as power and bandwidth. Wavelets are uniquely qualified to address this challenge. The flexibility and adaptation provided by wavelets have made wavelet technology a strong candidate for future wireless communication.