Manipulating the isofrequency curves of materials can effectively improve the interaction between light and matter. In recent years, based on the hyperbolic metamaterials, it has been widely proved that the topological phase transition from closed circle to open hyperbola will strongly affect the light transmission and radiation. In this review, a new type of anisotropic metamaterials, Linear-Crossing Metamaterials (LCMMs), which exist in hyperbolic topological transition is introduced. Because the signs of the in-plane permeabilities are opposite and the permittivity tends to zero, an LCMM may simultaneously possess the characteristics of an hyperbolic medium and a zero-index medium. On one hand, LCMMs support high-k modes just like hyperbolic medium because of the open iso-frequency contours. On the other hand, the linear dispersion relationship of the LCMMs ensures that the group velocity is perpendicular to the phase velocity, which leads to the zero phase accumulation along the propagation path just as in a zero-index medium. In addtion, LCMMs can have many unique properties. For example, considering that the signs of the in-plane permeability can also be tuned, two kinds of LCMMs with positive and negative refractions will be realized. Moreover, the refraction angle of incident light will be locked in two fixed directions that are independent of the incident angles. For a vertical incident beam incident on the LCMM, it will split into two beams just as does the valley-dependent propagation in photonic crystals. Due to the fact that the refracted light is locked in the two fixed directions, the propagation of light will not be affected when we put a defect inside the structure so long as it is not placed in the path of refraction. This property can be utilized for a partial cloaking effect that is robust to the presence of defects. LCMMs can also be used to realize the non-diffraction Bessel beam possessing unique self-healing properties. By mean of directional propagation and negative refraction, a point source instead of the plane wave can realize the Bessel beam through a planar LCMM. In a word, LCMM is a very interesting research topic and a wide range of potential applications based on LCMMs need to be explored. Especially, the realization, novel physical properties and important applications of linear-crossing metamaterials are summarized. Finally, the development of the research on linear-crossing metamaterials is prospected.