Current technology is producing high throughput biomedical data at an ever-growing rate. A common approach to interpreting such data is through network-based analyses. Since biological networks are notoriously complex and hard to decipher, a growing body of work applies graph embedding techniques to simplify, visualize, and facilitate the analysis of the resulting networks. In this review, we survey traditional and new approaches for graph embedding and compare their application to fundamental problems in network biology with using the networks directly. We consider a broad variety of applications including protein network alignment, community detection, and protein function prediction. We find that in all of these domains both types of approaches are of value and their performance depends on the evaluation measures being used and the goal of the project. In particular, network embedding methods outshine direct methods according to some of those measures and are, thus, an essential tool in bioinformatics research.Frontiers in Genetics | www.frontiersin.org Additionally, the learned embeddings are often applicable for downstream analysis, either by direct interpretation of the embedding space or through the application of machine learning techniques which are designed for vectorial data. Beyond its computational advantages, network embedding is natural to use in biological problems that concern physical entities (such as proteins) that function in 3D space. In such scenarios, Euclidean representations may capture many of the functional properties of those entities. Finally, by working in lower dimensional space, the results are more likely to be robust to the noise inherently present in the networks. Indeed, recent network denoising approaches employed embedding for this purpose .In this review, we describe several current approaches for graph embedding including spectral-based, diffusion-based and deep-learning-based methods. We provide comparisons applying representative embedding approaches to fundamental problems in network biology with using the networks directly in three distinct tasks: protein network alignment, protein module detection, and protein function prediction (Figure 1). We further review network embedding methods and their application to network denoising and pharmacogenomics. We conclude that network embedding methods are an essential component in the bioinformatics tool box.