This review discusses the development of new energy storage technologies that combine the advantages of batteries and electrochemical capacitors. Current energy storage systems, such as lithium-ion batteries and electrochemical capacitors (ECs), have limitations in energy density, power density, and cycle life. The review highlights the need for new materials and device architectures that can overcome these limitations and achieve a true hybridization of batteries and ECs. The review emphasizes the importance of understanding the fundamental mechanisms of energy storage at the atomic and molecular levels, as well as the role of materials design in achieving high energy and power densities. The review discusses the differences between batteries, pseudocapacitors, and ECs, focusing on the mechanisms of charge storage. It highlights the importance of materials with high surface area, such as porous carbons, for ECs, and the role of redox reactions in pseudocapacitors. The review also discusses the importance of crystallographic pathways in enabling efficient ion transport and the potential of 2D and 3D materials for energy storage applications. The review discusses the development of asymmetric and hybrid devices, which combine the advantages of both batteries and ECs. These devices can achieve high energy and power densities, making them suitable for a wide range of applications. The review also discusses the importance of electrode design, including the use of 3D architectures to improve ion access and reduce diffusion limitations. The review highlights the potential of multi-electron redox processes for improving the energy density of energy storage systems. It discusses the development of new cathode materials, such as transition metal oxides and chalcogenides, which can offer higher capacities and better performance. The review also discusses the importance of redox-active electrolytes in improving the energy density of energy storage systems. The review concludes by emphasizing the importance of computational methods in the design and development of new energy storage technologies. These methods can help identify promising materials and architectures, and provide insights into the fundamental mechanisms of energy storage. The review highlights the potential of computational materials science in the search for new materials with optimal properties for energy storage applications.This review discusses the development of new energy storage technologies that combine the advantages of batteries and electrochemical capacitors. Current energy storage systems, such as lithium-ion batteries and electrochemical capacitors (ECs), have limitations in energy density, power density, and cycle life. The review highlights the need for new materials and device architectures that can overcome these limitations and achieve a true hybridization of batteries and ECs. The review emphasizes the importance of understanding the fundamental mechanisms of energy storage at the atomic and molecular levels, as well as the role of materials design in achieving high energy and power densities. The review discusses the differences between batteries, pseudocapacitors, and ECs, focusing on the mechanisms of charge storage. It highlights the importance of materials with high surface area, such as porous carbons, for ECs, and the role of redox reactions in pseudocapacitors. The review also discusses the importance of crystallographic pathways in enabling efficient ion transport and the potential of 2D and 3D materials for energy storage applications. The review discusses the development of asymmetric and hybrid devices, which combine the advantages of both batteries and ECs. These devices can achieve high energy and power densities, making them suitable for a wide range of applications. The review also discusses the importance of electrode design, including the use of 3D architectures to improve ion access and reduce diffusion limitations. The review highlights the potential of multi-electron redox processes for improving the energy density of energy storage systems. It discusses the development of new cathode materials, such as transition metal oxides and chalcogenides, which can offer higher capacities and better performance. The review also discusses the importance of redox-active electrolytes in improving the energy density of energy storage systems. The review concludes by emphasizing the importance of computational methods in the design and development of new energy storage technologies. These methods can help identify promising materials and architectures, and provide insights into the fundamental mechanisms of energy storage. The review highlights the potential of computational materials science in the search for new materials with optimal properties for energy storage applications.