Today's computing architectures and device technologies are unable to meet the increasingly stringent demands on energy and performance posed by emerging applications. Therefore, alternative computing architectures are being explored that leverage novel post-CMOS device technologies. One of these is a Computation-in-Memory architecture based on memristive devices. This paper describes the concept of such an architecture and shows different applications that could significantly benefit from it. For each application, the algorithm, the architecture, the primitive operations, and the potential benefits are presented. The applications cover the domains of data analytics, signal processing, and machine learning.