Graph matching, which refers to a class of computational problems of finding an optimal correspondence between the vertices of graphs to minimize (maximize) their node and edge disagreements (affinities), is a fundamental problem in computer science and relates to many areas such as com- binatorics, pattern recognition, multimedia and computer vision. Compared with the exact graph (sub)isomorphism often considered in a theoretical setting, inexact weighted graph matching receives more attentions due to its flexibility and practical utility. A short review of the recent re- search activity concerning (inexact) weighted graph matching is presented, detailing the methodologies, formulations, and algorithms. It highlights the methods under several key bullets, e.g. how many graphs are involved, how the affinity is modeled, how the problem order is explored, and how the matching procedure is conducted etc. Moreover, the research activity at the forefront of graph matching applications especially in computer vision, multimedia and machine learning is reported. The aim is to provide a systematic and compact framework regarding the recent development and the current state-of-the-arts in graph matching.