Majorana fermions (MF) obey non-Abelian statistics and have potential applications in topological quantum computation and quantum information processing. Several types of hybrid devices that can possibly host MFs in low-latitude condensed matter systems have been proposed in the last decade, including hybrid semiconductor nanowire/superconductor devices, iron chains on the superconducting surface, hybrid iron-based superconductor, and topological insulator/superconductor structures, with the analogous Majorana signals have been observed in the above hybrid system with different electrical means. And the proposal that there may be Majorana fermions in topological insulators has attracted much attention. Although a mass of theoretical schemes have been proposed consecutively, and similar Majorana signatures have been experimentally demonstrated, no conclusive evidence of the existence of MFs in low-latitude condensed matter systems is available and MFs-based topological quantum computing is difficult to achieve. In this review, we introduce several schemes for detecting MFs in low-latitude condensed matter systems, as well as elaborate on the different electrical means for probing MFs. Most MFs detection schemes focus on electronic transport properties recently, and in order to obtain more conclusive evidence of MFs, it is necessary to propose alternative methods for detecting MFs. Alternative setups or proposals for detecting MFs are thus required to obtain definitive signatures of MFs. We introduced an all-optical pump-probe technology accompanying hybrid micro- and nano-systems, and proposed a series of all-optical methods for detecting MFs, benefiting from recent progress in nanotechnology. Moreover, we also review the optical detection of MFs and MFs-induced coherent optical propagation. Finally, we anticipate quantum computation using MFs in solid-state quantum devices.