Computing-in-memory (CIM) has emerged as an energy-efficient hardware solution for machine learning and AI. While static random access memory (SRAM)-based CIM has been prevalent, growing attention is directed towards leveraging dynamic random access memory (DRAM) and non-volatile memory (NVM) with its unique characteristics such as high-density and non-volatility. This brief reviews the evolving trends in DRAM and NVM-based CIM, which have faced unique challenges that arise from SRAM despite their advantages. For instance, the DRAM cell's density comes with leakage and refresh issues, impacting efficiency and computing accuracy. NVM-CIM faces computing accuracy challenges of resistance-based computation with low signal margins and non-linear characteristics. This tutorial discusses the current status and future directions in DRAM-CIM and NVM-CIM research, which address the abovementioned challenge.