The AdS/CFT correspondence between Sasaki-Einstein spaces and 4D superconformal field theories is discussed. At the algebraic level, the connection between toric data, brane dimers and quiver diagrams is analysed. Various quantitative checks of the duality can be performed in the BPS sector, including mesonic and baryonic states. Some applications, such as exactly marginal deformations and semiclas-sical strings, will also be discussed.