Cloud computing (CC) has recently been receiving tremendous attention from the IT industry and academic researchers. CC leverages its unique services to cloud customers in a pay-as-you-go, anytime, anywhere manner. Cloud services provide dynamically scalable services through the Internet on demand. Therefore, service provisioning plays a key role in CC. The cloud customer must be able to select appropriate services according to his or her needs. Several approaches have been proposed to solve the service selection problem, including multicriteria decision analysis (MCDA). MCDA enables the user to choose from among a number of available choices. In this paper, we analyze the application of MCDA to service selection in CC. We identify and synthesize several MCDA techniques and provide a comprehensive analysis of this technology for general readers. In addition, we present a taxonomy derived from a survey of the current literature. Finally, we highlight several state-of-the-art practical aspects of MCDA implementation in cloud computing service selection. The contributions of this study are four-fold: (a) focusing on the state-of-the-art MCDA techniques, (b) highlighting the comparative analysis and suitability of several MCDA methods, (c) presenting a taxonomy through extensive literature review, and (d) analyzing and summarizing the cloud computing service selections in different scenarios.