With the rise of the Internet of Things (IoT), a huge market for so-called smart edge-devices is foreseen for millions of applications, like personalized healthcare and smart robotics. These devices have to bring smart computing directly where the data is generated, while coping with the limited energy budget. Conventional von-Neumann architecture fail to meet these requirements due to e.g., memory-processor data transfer bottleneck. Memristor-based computation-in-memory (CIM) has the potential to realize smart local computing for highly parallel data-dominated AI applications by exploiting the inherent properties of the architecture and the physical characteristics of the memristors. This paper provides a broad overview of CIM architecture highlighting its potential and unique properties in enabling smart local computing. Moreover, it discusses design considerations of such architectures including both crossbar array as well as peripheral circuits; special attention is given to analog-to-digital converter (ADC), as it is the most critical unit of analog-based CIM operation e.g., vector-matrix multiplication (VMM). Finally, the paper outlines the potential future directions for CIM-based edge smart computing.