Phase field modeling and computer simulation is employed to study the relations between filler microstructures and effective properties of dielectric composites. The model solves electrostatic equations in terms of polarization vector field in reciprocal space using a fast Fourier transform technique and parallel computing algorithm. Composites composed of linear constituent phases of different dielectric constants are considered. Interphase boundary conditions are automatically taken into account without explicitly tracking interphase interfaces in the composites. Various factors associated with filler microstructures are systematically investigated, including dielectric constant mismatch between fillers and matrix, particle size, shape, orientation, volume fraction, and spatial arrangement as well as directional alignment. Heterogeneous distributions of polarization, charge density, and local electric field are calculated for each composite microstructure, based on which effective dielectric constant and dielectric anisotropy of the composites are determined. It is found that electrostatic interactions among high-dielectric-constant fillers embedded in low-dielectric-constant matrix play critical roles in determining the composite properties, which sensitively depend on filler arrangement and, especially, directional alignment into fibrous microstructures (chains). Such microstructurally engineered composites, whose fillers are not randomly dispersed, exhibit strong dielectric anisotropy despite all constituent components being isotropic.