Graph technologies allow modeling of complex relationships and connections through nodes and edges. There are three main layers of graph technologies: graph databases to store graph data, graph analysis frameworks to analyze large graphs, and graph visualization solutions to interact with graphs. Popular tools in each layer include Neo4j and Titan for databases, Giraph and GraphX for analysis, and Gephi and Cytoscape for visualization. Graph technologies are gaining more attention due to their ability to extract insights from connected data.