  We review the paradigm of holographic dark energy (HDE), which arises from a
theoretical attempt of applying the holographic principle (HP) to the dark
energy (DE) problem. Making use of the HP and the dimensional analysis, we
derive the general formula of the energy density of HDE. Then, we describe the
properties of HDE model, in which the future event horizon is chosen as the
characteristic length scale. We also introduce the theoretical explorations and
the observational constraints for this model. Next, in the framework of HDE, we
discuss various topics, such as spatial curvature, neutrino, instability of
perturbation, time-varying gravitational constant, inflation, black hole and
big rip singularity. In addition, from both the theoretical and the
observational aspects, we introduce the interacting holographic dark energy
scenario, where the interaction between dark matter and HDE is taken into
account. Furthermore, we discuss the HDE scenario in various modified gravity
(MG) theories, such as Brans-Dicke theory, braneworld theory, scalar-tensor
theory, Horava-Lifshitz theory, and so on. Besides, we introduce the attempts
of reconstructing various scalar-field DE and MG models from HDE. Moreover, we
introduce other DE models inspired by the HP, in which different characteristic
length scales are chosen. Finally, we make comparisons among various
HP-inspired DE models, by using cosmological observations and diagnostic tools.
