A non-volatile memory having boost structures. Boost structures are provided for individual NAND strings and can be individually controlled to assist in programming, verifying and reading processes. The boost structures can be commonly boosted and individually discharged, in part, based on a target programming state or verify level. The boost structures assists in programming so that the programming and pass voltage on a word line can be reduced, thereby reducing side effects such as program disturb. During verifying, all storage elements on a word line can be verified concurrently. The boost structure can also assist during reading. In one approach, the NAND string has dual source-side select gates between which the boost structure contacts the substrate at a source/drain region, and a boost voltage is provided to the boost structure via a source-side of the NAND string.