Dielectrics are electrical insulator materials, polarizable by opposite displacement of positive and negative ionized atoms via electric fields across the material’s thickness. Dielectrics are used in energy-storage capacitors, as key components in modern micro-/nanoelectronics, high-frequency and mobile communication devices, and life-saving microchips and other devices such as defibrillators and pacemakers implantable in humans. A key dielectric parameter is the dielectric constant (k), which largely controls the capacitance in capacitors with nanoscale area and dielectric layer thickness. Extremely high dielectric constants (k ≥1000) were observed in oxides (e.g., La1.8Sr0.12NiO4) with relaxor/ferroelectric materials and in combined semiconducting bulk properties with highly resistive grain boundaries. Giant dielectric constant films have also been demonstrated, based on integrating relatively low-dielectric-constant oxides into nanolaminate structures (e.g., TiOx/Al2O3; TiO2/HfO2) with tailored sublayer thicknesses, interfaces, and oxygen atom distributions. This overview article addresses the science and technology of high-dielectric-constant oxide materials with different compositions and structures.