During the recent years, the iron-based superconductors with a topological band structure have attracted intensive attention from the science community as a new and promising platform for emerging Majorana zero modes in their vortex core. These topological iron-based superconductors possess all of the desirable properties, i.e. single material, high-T_c superconductivity, strong electron-electron correlation and topological band structure, thus successfully avoiding the difficulties suffered by previous Majorana platforms, such as intrinsic topological superconductors and multiple types of proximitized heterostructures. So far, one has observed pristine vortex Majorana zero modes in several different compounds of iron-based superconductors. The systematic studies performed on those systems show that the vortex Majorana zero modes are quite evident experimentally and very clear theoretically, leading to a bright future in applications. The vortex cores of iron-based superconductors can become one of the major candidates for exploring topological quantum computing in the future. In this review article, we will focus on Fe(Te, Se) single crystal, to introduce the original ideas and research progress of the new emerging “iron home” for Majorana zero modes. Having elabrated the basic band structures and the experimental facts of the observed vortex zero modes in Fe(Te, Se), we will systematically summarize the main observations and fundamental physics of vortex Majorana zero modes in Fe(Te, Se). First of all, with the help of the observed behavior of Majorana wavefunction and quasiparticle poisioning, we will analyze the emerging mechanism of vortex Majorana zero modes in Fe(Te, Se). Then we will elaborate the measurements on Majorana symmetry and topological nature of vortex Majorana zero modes, assisted by several existing Majorana theories. After that, we will switch our view angle from quantum physics to quantum engineering, and comprehensively analyze the fate of vortex Majorana zero modes in a real material under a real environment, which may benefit the potential engineering applications in the future. This review article follows the physical properties of vortex Majorana zero modes, and emphasizes the link between theories and experiments. Our goal is to bridge the gap between the classical Majorana theories and the new emerging Majorana platform in iron-based superconductors, and help the readers to understand the experimental observations of the newly discovered “iron home” for Majoranas.