Chiplet-based multi-chip integration designs provide a flexible and scalable solution that surpasses traditional SoC (System on Chip) monolithic integration. However, inter-chiplet communication has become a significant bottleneck affecting overall system performance. The Network on Interposer (NoI) plays a pivotal role in multi-chip systems, directly influencing both performance and development costs. In this paper, we review NoI communication topologies for heterogeneous chiplets. We thoroughly explore the importance of current inter-chiplet communication architectures and discuss their design and implementation methods. This paper covers the entire communication process, spanning from protocol and interface layers to the application layer, classifying interconnect topologies based on their structural configurations and providing in-depth analyses and cross-comparisons for each category. Furthermore, we investigate future directions in NoI communication technologies, identifying technical challenges and potential solutions. We also propose advanced evaluation methods and modeling techniques for reusable interposer layers and topologies. This review aims to provide researchers with a thorough understanding of the current landscape and future trends in NoI technology, emphasizing its crucial role in advancing next-generation semiconductor devices across a wide spectrum of applications.