Integrated photonic platforms have rapidly emerged as highly promising and extensively investigated systems for advancing classical and quantum information technologies, since their ability to seamlessly integrate photonic components within the telecommunication band with existing silicon-based industrial processes offers significant advantages. However, despite this integration facilitating the development of novel devices, fostering fast and reliable communication protocols and the manipulation of quantum information, traditional integrated silicon photonics faces inherent physical limitations that necessitate a challenging trade-off between device efficiency and spatial footprint. To address this issue, researchers are focusing on the integration of nanoscale materials into photonic platforms, offering a novel approach to enhance device performance while reducing spatial requirements. These developments are of paramount importance in both classical and quantum information technologies, potentially revolutionizing the industry. In this review, we explore the latest endeavors in hybrid photonic platforms leveraging the combination of integrated silicon photonic platforms and nanoscale materials, allowing for the unlocking of increased device efficiency and compact form factors. Finally, we provide insights into future developments and the evolving landscape of hybrid integrated photonic nanomaterial platforms.