Networks are one of the most powerful structures for modeling problems in the real world. Downstream machine learning tasks defined on networks have the potential to solve a variety of problems. With link prediction, for instance, one can predict whether two persons will become friends on a social network. Many machine learning algorithms, however, require that each input example is a real vector. Network embedding encompasses various methods for unsupervised, and sometimes supervised, learning of feature representations of nodes and links in a network. Typically, embedding methods are based on the assumption that the similarity between nodes in the network should be reflected in the learned feature representations. In this paper, we review significant contributions to network embedding in the last decade. In particular, we look at four methods: Spectral Clustering, DeepWalk, Large-scale Information Network Embedding (LINE), and node2vec. We describe each method and list its advantages and shortcomings. In addition, we give examples of real-world machine learning problems on networks in which the embedding is critical in order to maximize the predictive performance of the machine learning task. Finally, we take a look at research trends and state-of-the art methods in the research on network embedding.