Graph networks can model data observed across different levels of biological systems that span from population graphs (with patients as network nodes) to molecular graphs that involve omics data. Graph-based approaches have shed light on decoding biological processes modulated by complex interactions. This paper systematically reviews graph-based analysis methods of Graph Signal Processing (GSP), Graph Neural Networks (GNNs) and graph topology inference, and their applications to biological data. This work focuses on the algorithms of graph-based approaches and the constructions of graph-based frameworks that are adapted to a broad range of biological data. We cover the Graph Fourier Transform and the graph filter developed in GSP, which provides tools to investigate biological signals in the graph domain that can potentially benefit from the underlying graph structures. We also review the node, graph, and interaction oriented applications of GNNs with inductive and transductive learning manners for various biological targets. As a key component of graph analysis, we provide a review of graph topology inference methods that incorporate assumptions for specific biological objectives. Finally, we discuss the biological application of graph analysis methods within this exhaustive literature collection, potentially providing insights for future research in biological sciences.