1-3 piezocomposites are excellent candidate materials for sensor, actuator and transducer applications owing to their remarkable dielectric properties, enhanced piezoelectric coupling constants and improved hydrostatic performance along with tunable acoustic impedance, high bandwidth and reliability. These materials find extensive use in aerospace, naval and biomedical sectors. 1-3 piezocomposites show a linear response when subjected to low electric fields and/or mechanical stresses. In such cases, linear models are sufficient for predicting their linear response. But, when high electro-mechanical loads are applied to these materials, they show nonlinearity owing to the presence of a passive and viscoelastic polymer matrix phase and inherent hysteretic damping in the piezoceramic fibers. This is when it becomes mandatory to understand both their linear and nonlinear behavior under different magnitudes of thermo-electro-mechanical static and dynamic loads. Linear response is modeled using linear piezoelectric constitutive equations. Nonlinearities in the form of hysteresis, depolarization, fatigue and creep occurs in 1-3 piezocomposites, which drastically affects their accuracy, precision and efficiency. In order to understand these nonlinearities, analytical and numerical methods have been proposed by several researchers in the past. An endeavor has been undertaken to review some of the attempts made earlier in these directions. Effective properties of these inhomogeneous media are evaluated through different hypotheses and assumptions. Most often, experimental routes are undertaken to predict material properties of 1-3 piezocomposites; nevertheless, the experimental evaluation of a few material properties is quite difficult and sometimes impossible, even with the best state-of-the-art experimental facilities. This motivates researchers to develop theoretical models to predict these material properties. Nonlinearities in 1-3 piezocomposites have been studied by researchers earlier with different theoretical modeling approaches and experimental techniques. This review paper is an endeavor to discuss the progress regarding the study of effective properties and nonlinearities in 1-3 piezocomposites in a coherent and holistic manner. © 2019 IOP Publishing Ltd.