For a long time, it has been generally acknowledged that low-dimensional (lower than three-dimensions) long-range orders cannot stay stable at any finite temperature, because temperature-induced fluctuations can destroy any long-range orders in low-dimensional systems supported by isotropic short-range interactions. However, this theorem requires that the interaction must be short-range and isotropic. In fact, many low-dimensional systems do not meet these two requirements. For example, due to the strong anisotropy in two-dimensional CrI₃ crystals, there is a band gap in the magnon spectrum. When the excitation energy from temperature is much lower than the band gap, the magneton cannot be excited by temperature on a large scale, and the long-range magnetic order in the two-dimensional system will not be destroyed. Various methods have been used to characterize the magnetic order in atomically thin CrI₃ crystals, and a lot of attempts have been made to manipulate the magnetic structure in the system. Focusing on CrI₃, in this article we review the recent studies on growth, magnetic structure measurement and manipulation of two-dimensional magnetic materials, and also discuss the prospects for the next phase of research from the perspectives of basic condensed matter physics research and electronic engineering applications.