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High energy density, high temperature, and low loss polymer dielectrics are highly desirable for electric energy storage, e.g., film capacitors in the power electronics of electric vehicles and high-speed trains. Fundamentally, high polarization and low dielectric loss are two conflicting physical properties, because more polarization processes will involve more loss mechanisms. As such, we can only achieve a delicate balance between high dielectric constant and reasonably low loss. This review focuses on achieving low dielectric loss while trying to enhance dielectric constants for dielectric polymers, which can be divided into two categories: extrinsic and intrinsic. For extrinsic dielectric systems, the working mechanisms include dipolar (e.g., nanodielectrics) and space charge (e.g., ion gels) interfacial polarizations. These polarizations do not increase the intrinsic dielectric constants, but cause decreased breakdown strength and increased dielectric loss for polymers. For intrinsic dielectric polymers, the dielectric constant originates from electronic, atomic (or vibrational), and orientational polarizations, which are intrinsic to the polymers themselves. Because of the nature of molecular bonding for organic polymers, the dielectric constant from electronic and atomic polarizations is limited to 2-5 for hydrocarbon-based insulators (i.e., band gap > 4 eV). It is possible to use orientational polarization to enhance intrinsic dielectric constant while keeping reasonably low loss. However, nonlinear ferroelectric switching in ferroelectric polymers must be avoided. Meanwhile, paraelectric polymers often exhibit high electronic conduction due to large chain motion in the paraelectric phase. In this sense, dipolar glass polymers are more attractive for low loss dielectrics, because frozen chain dynamics enables deep traps to prevent electronic conduction. Both side-chain and main-chain dipolar glass polymers are promising candidates. Furthermore, it is possible to combine intrinsic and extrinsic dielectric properties synergistically in multilayer films to enhance breakdown strength and further reduce dielectric loss for high dielectric constant polar polymers. At last, future research directions are briefly discussed for the ultimate realization of next generation polymer film capacitors.