Array signal processing technology is an important part in the field of signal processing, which is widely used in radar, sonar and hydropower astronomy. Spatial spectrum estimation is a major research hotspot in array signal processing and is confined to the arrays with interelement spacing smaller than half wavelength of the carrier wave to avoid ambiguous angles. Generally, the interelement spacing of coprime arrays is larger than half wavelength. As a result, with fixed number of sensors, the coprime arrays can obtain extended array aperture and hence the corresponding spectrum estimation methods can achieve better direction of arrival estimation performance and resolution, where the targets can be detected uniquely with coprime property. Therefore, the investigations of spatial spectrum estimation with coprime arrays have aroused considerable attentions in array signal processing. In this paper, we summarize the existing researches based on coprime linear array and coprime planar array and analysis the advantages of the coprime array relative to the uniform array in expanding array aperture and increasing spatial degree of freedom. Simulation results validate the effectiveness and superiority of the methods with coprime arrays.