Discharge phenomena, from electrostatic discharges in integrated circuits to lightning in the atmosphere, are pervasive and can lead to economic consequences in the electronic industry. Among these, partial discharge (PD) is a critical factor causing insulation damage in power equipment, significantly impacting power networks. Moreover, due to the trend of digitization, the number of pieces of power equipment has significantly increased. Real-time online monitoring of equipment can alleviate the impact of unavoidable PD events, and its necessity is significantly enhanced. In response, co-designing advanced materials, non-volatile memory (NVM), and software (SW) for discharge monitoring offers a compelling solution. This is achieved through an integrated sensing–memory–computation system. This review thoroughly examines different technologies used for monitoring PD, focusing on how sensing, memory, and computation play a role. It also looks at the possible difficulties and future expectations when SW and hardware technologies are combined in these systems. The solution to the three challenges of energy consumption, dedicated architecture, and circuit aging in integrated systems will greatly improve the energy efficiency, processing speed, and service life of intelligent monitoring systems. Eventually, this provides a feasible strategy for designing systems that can efficiently reduce the negative impacts of PD through smart monitoring and analysis.