Recently, there has been significant interest toward the development of tunable dielectric materials for voltage-controlled, frequency-agile phase shifters and filters operating in the microwave regime. The fundamental challenge in designing materials systems for such tunable devices is the simultaneous requirement of high dielectric tunability (> 40%) over a large temperature interval (-10 A degrees C to +90 A degrees C) coupled with low dielectric losses (between 3.0 dB and 4.0 dB in operational bandwidths ranging from several hundred MHz up to 30 or more GHz). We show that a high- and temperature-insensitive tunability can be realized in compositionally graded ferroelectrics and provide a brief review of the results of experimental and theoretical studies on the dielectric properties of Barium Strontium Titanate (Ba1-x Sr (x) TiO3 or BST) multilayer heterostructures. Theoretically, we discuss the role of thermal stresses on the dielectric properties using a non-linear thermodynamic model coupled with basic electrostatic considerations to describe the interlayer interactions between the ferroelectric layers. We show that the thermal strains arising from the thermal expansion coefficient mismatch between the multilayered film and the substrate may have a significant effect on the dielectric permittivity and tunability of BST multilayers. Experimentally, compositionally graded BST multilayers (5 mol% MgO doped and undoped) were grown via metallo-organic solution deposition (MOSD) on Pt-Si substrates and electrically characterized. Optimum conditions were found to exist in BST multilayers consisting of three distinct layers of similar to 220 nm nominal thickness with compositions corresponding to Ba0.60Sr0.40TiO3 (BST 60/40), BST 75/25, and BST 90/10. At room temperature, the BST heterostructure has a small-signal dielectric permittivity of 360 with a dissipation factor of 0.012 and a dielectric tunability of 65% at 444 kV/cm. These properties exhibit minimal dispersion as a function of temperature ranging from 90 A degrees C to -10 A degrees C. Our results also show that MgO doping improves dielectric loss (tan delta = 0.008), but results in a moderate dielectric tunability of 29% at 444 kV/cm. Electrical measurements at microwave frequencies display a decrease in the dielectric permittivity and tunability for both undoped and MgO-doped BST multilayers. At 10 GHz, the dielectric response, tunability, and the loss characteristics for graded undoped BST are 261, 25% (at 1,778 kV/cm), and 0.078, respectively, and 189 and 15% (at 1,778 kV/cm), and 0.039, respectively, for the MgO-doped graded BST.