The article discusses the concept of in-memory computing, which involves performing computational tasks directly in the memory itself by leveraging the physical attributes of memory devices. This approach aims to reduce the latency and energy costs associated with data movement, a significant bottleneck in traditional von Neumann computing systems, especially for data-centric applications like artificial intelligence. The review covers both charge-based and resistance-based memory devices, including DRAM, SRAM, Flash, RRAM, PCM, and MRAM. These devices are organized in arrays and can perform various computational tasks such as matrix-vector multiplication (MVM), logical operations, and optimization problems. The article also explores applications of in-memory computing in scientific computing, signal processing, optimization, machine learning, deep learning, and stochastic computing. Challenges and opportunities in these areas are discussed, highlighting the need for improved device properties and efficient algorithms to fully realize the potential of in-memory computing.The article discusses the concept of in-memory computing, which involves performing computational tasks directly in the memory itself by leveraging the physical attributes of memory devices. This approach aims to reduce the latency and energy costs associated with data movement, a significant bottleneck in traditional von Neumann computing systems, especially for data-centric applications like artificial intelligence. The review covers both charge-based and resistance-based memory devices, including DRAM, SRAM, Flash, RRAM, PCM, and MRAM. These devices are organized in arrays and can perform various computational tasks such as matrix-vector multiplication (MVM), logical operations, and optimization problems. The article also explores applications of in-memory computing in scientific computing, signal processing, optimization, machine learning, deep learning, and stochastic computing. Challenges and opportunities in these areas are discussed, highlighting the need for improved device properties and efficient algorithms to fully realize the potential of in-memory computing.