and their potential applications in various fields, including optical waveguiding, imaging, ultrasensitive optical sensing, and electromagnetic cloaking.Among the different types of optical metamaterials proposed and demonstrated to date, there is one class of highly anisotropic metamaterials which exhibit hyperbolic (or indefinite) dispersions, depending on their effective electric tensors (here, we only consider nonmagnetic media with unit magnetic tensors). Such hyperbolic metamaterials (HMMs) have reached the ultra-anisotropic limit of traditional uniaxial crystal and lead to dramatic changes for the light propagation behaviors. [12][13][14][15][16] Compared with other optical metamaterials, like chiral [17,18] and split ring resonator-based metamaterials, [19,20] HMMs have advantages of relative ease of fabrication at optical frequencies, broadband nonresonant and 3D bulk responses, and flexible wavelength tunability. As a result, HMMs have attracted widespread interest and become a good multifunctional platform for many exotic applications, such as optical negative refraction and light beam steering, [12,[21][22][23][24][25][26][27][28] subdiffraction-limited imaging and nanolithography, [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] spontaneous and thermal emission engineering, [71][72][73][74][75][76][77][78][79][80] ultrasensitive optical, biological, and chemical sensing, [81][82][83][84][85][86][87][88][89] omnidirectional and broadband optical absorption. [90][91][92][93] On the other hand, ultrathin metasurfaces, which comprise a class of planar optical metamaterials with many subwavelength structural units, have attracted much attention due to their ability of locally controlling the phase, amplitude, and polarization of light at the interface between two natural materials. [94][95][96][97] 2D planar metasurfaces have many advantages over bulk metamaterials, including simplifying the fabrication and integration process, reducing energy loss, and being compatible with other photonics devices. In this context, as an efficient surface wave modulation platform, hyperbolic metasurfaces (HMSs) with in-plane hyperbolic dispersions have a potential influence on the development of on-chip planar photonic devices. [95,98] In this review, we first discuss the dispersions and realizations of hyperbolic media. Then, we review the recent achievements of various optical applications based on 3D bulk HMMs and 2D planar HMSs. It should be stressed that, although some application scenarios for 3D HMMs and 2D HMSs are analogous, in fact they are not equal to each other because additional constrains will be introduced on the surface wave as the dimensionality degraded, which is accompanied by fancy in-plane Recent advances in nanofabrication and characterization technologies have spurred many breakthroughs in the field of optical metamaterials and metasurfaces that provide novel ways of manipulating light interaction in a well controllable manner. Among these artificial nanostructured materials, ...