Polymers are long-chain, highly molecular weight molecules containing large numbers of repeating units within their backbone derived from the product of polymerization of monomeric units. The materials exhibit unique properties based on the types of bonds that exist within their structures. Among these, some behave as rubbers because of their excellent bending ability, lightweight nature, and shape memory. Moreover, their tunable chemical, structural, and electrical properties make them promising candidates for their use as sensing materials. Polymer-based sensors are highly utilized in the current scenario in the public health sector and environment control due to their rapid detection, small size, high sensitivity, and suitability in atmospheric conditions. Therefore, the aim of this review article is to highlight the current progress in polymer-based sensors. More importantly, this review provides general trends and challenges in sensor technology based on polymer materials.