The transmission of massive amounts of small packets generated by access networks through high-speed Internet core networks to other access networks or cloud computing data centres has introduced several challenges such as poor throughput, underutilisation of network resources, and higher energy consumption. Therefore, it is essential to develop strategies to deal with these challenges. One of them is to aggregate smaller packets into a larger payload packet, and these groups of aggregated packets will share the same header, hence increasing throughput, improved resource utilisation, and reduction in energy consumption. This paper presents a review of packet aggregation applications in access networks (e.g., IoT and 4G/5G mobile networks), optical core networks, and cloud computing data centre networks. Then we propose new analytical models based on diffusion approximation for the evaluation of the performance of packet aggregation mechanisms. We demonstrate the use of measured traffic from real networks to evaluate the performance of packet aggregation mechanisms analytically. The use of diffusion approximation allows us to consider time-dependent queueing models with general interarrival and service time distributions. Therefore these models are more general than others presented till now.