Learning the representations of nodes in a network can benefit various analysis tasks such as node classification, link prediction, clustering, and anomaly detection. Such a representation learning problem is referred to as network embedding, and it has attracted significant attention in recent years. In this article, we briefly review the existing network embedding methods by two taxonomies. The technical taxonomy focuses on the specific techniques used and divides the existing network embedding methods into two stages, i.e., context construction and objective design. The non-technical taxonomy focuses on the problem setting aspect and categorizes existing work based on whether to preserve special network properties, to consider special network types, or to incorporate additional inputs. Finally, we summarize the main findings based on the two taxonomies, analyze their usefulness, and discuss future directions in this area.