Higher-order band topology not only enriches our understanding of topological phases but also unveils pioneering lower-dimensional boundary states, which harbors substantial potential for next-generation device applications. The distinct electronic configurations and tunable attributes of two-dimensional materials position them as a quintessential platform for the realization of second-order topological insulators (SOTIs). This article provides an overview of the research progress in SOTIs within the field of two-dimensional electronic materials, focusing on the characterization of higher-order topological properties and the numerous candidate materials proposed in theoretical studies. These endeavors not only enhance our understanding of higher-order topological states but also highlight potential material systems that could be experimentally realized.