This article addresses the past, present, and future status of hybrid plasmonic waveguides (HPWs). It presents a comprehensive review of HPW-based photonic integrated circuits (PICs), covering both passive and active devices, as well as potential application of on-chip HPW-based devices. HPW-based integrated circuits (HPWICs) are compatible with complementary metal oxide semiconductor technology, and their matched refractive indices enables the adaptation of existing fabrication processes for silicon-on-insulator designs. HPWs combine plasmonic and photonic waveguide components to provide strong confinement with longer propagation length Lp of HP modes with nominal losses. These HPWs are able to make a trade-off between low loss and longer Lp, which is not possible with independent plasmonic and photonic waveguide components owing to their inability to simultaneously achieve low propagation loss with rapid and effective all-optical functionality. With HPWs, it is possible to overcome challenges such as high Ohmic losses and enhance the functional performance of PICs through the use of multiple discrete components. HPWs have been employed not only to guide transverse magnetic modes but also for optical beam manipulation, wireless optical communication, filtering, computation, sensing of bending, optical signal emission, and splitting. They also have the potential to play a pivotal role in optical communication systems for quantum computing and within data centers. At present, HPW-based PICs are poised to transform wireless chip-to-chip communication, a number of areas of biomedical science, machine learning, and artificial intelligence, as well as enabling the creation of densely integrated circuits and highly compact photonic devices.