In the realization of photonic integrated devices, materials such as polymers are crucial. Polymers have shown compatibility with several patterning techniques, are generally affordable, and may be functionalized to obtain desired optical, electrical, or mechanical characteristics. Polymer waveguides are a viable platform for optical connectivity since they are easily adaptable to on-chip and on-board integration and promise low propagation losses <1 dB/cm. Furthermore, polymer waveguides can be made to be extremely flexible, able to withstand bending, twisting, and even stretching. Optical sensing is an interesting field of research that is gaining popularity in polymer photonics. Due to its huge potential for use in several industries, polymer waveguide-based sensors have attracted a lot of attention. Due to their resilience to electromagnetic fields, optical sensors operate better in difficult situations, such as those found in electrical power generating and conversion facilities. In this review, the most widely used polymer materials are discussed for integrated photonics. Moreover, four significant sensing applications of polymer-waveguide based sensors which include biosensing, gas sensing, temperature sensing and mechanical sensing have been debated.