The emergence of multifunctional wearable electronics over the past decades has triggered the exploration of flexible energy storage devices. As an important component of flexible batteries, novel electrodes with good flexibility, mechanical stability and high energy density are required to adapt to mechanical deformation while powering devices. Electrodes with sophisticated designed structures are key to achieving novel batteries and supercapacitors with extended lifetimes under long-term deformation exposures. Many different novel structures including serpentine, auxetic and biomimetic are explored to construct electrodes thanks to their excellent mechanical deformability in three dimensions. This paper considers the various design strategies established for fabricating flexible electrodes using novel structural modifications. The current state-of-the-art developments of novel structures made of two-dimensional (2D) planar and three-dimensional (3D) cellular, interconnected architectures for flexible energy storage with different functionalities, are discussed. The key tunable geometrical parameters of structures for achieving high performance are critically assessed, and the challenges and limitations of electrodes facing their practical application are revealed, to offer new insights into future prospects of this field.