Among nanocomposite materials, multifunctional polymer nanocomposites have prompted important innovations in the field of sensing technology. Polymer-based nanocomposites have been successfully utilized to design high-tech sensors. Thus, conductive, thermoplast, or elastomeric, as well as natural polymers have been applied. Carbon nanoparticles as well as inorganic nanoparticles, such as metal nanoparticles or metal oxides, have reinforced polymer matrices for sensor fabrication. The sensing features and performances rely on the interactions between the nanocomposites and analytes like gases, ions, chemicals, biological species, and others. The multifunctional nanocomposite-derived sensors possess superior durability, electrical conductivity, sensitivity, selectivity, and responsiveness, compared with neat polymers and other nanomaterials. Due to the importance of polymeric nanocomposite for sensors, this novel overview has been expanded, focusing on nanocomposites based on conductive/non-conductive polymers filled with the nanocarbon/inorganic nanofillers. To the best of our knowledge, this article is innovative in its framework and the literature covered regarding the design, features, physical properties, and the sensing potential of multifunctional nanomaterials. Explicitly, the nanocomposites have been assessed for their strain-sensing, gas-sensing, bio-sensing, and chemical-sensing applications. Here, analyte recognition by nanocomposite sensors have been found to rely on factors such as nanocomposite design, polymer type, nanofiller type, nanofiller content, matrix–nanofiller interactions, interface effects, and processing method used. In addition, the interactions between a nanocomposite and analyte molecules are defined by high sensitivity, selectivity, and response time, as well as the sensing mechanism of the sensors. All these factors have led to the high-tech sensing applications of advanced nanocomposite-based sensors. In the future, comprehensive attempts regarding the innovative design, sensing mechanism, and the performance of progressive multifunctional nanocomposites may lead to better the strain-sensing, gas/ion-sensing, and chemical-sensing of analyte species for technical purposes.