Data movement is the dominant execution and energy cost across the application workloads in data centers and supercomputers. Programming at the tile level has become a popular strategy for optimizing data movement for both deep learning and general structured grids, using Triton, cuTile, bricks, and fine-grained data blocks. Expressing hierarchical data and thread layouts, mostly designed with matrix processors in mind, facilitates automatic code generation that further raises the level of abstraction in such code. In this talk, we will describe prior work on BrickLib supporting fine-grained data blocks and active research on LEGO for hierarchical data and thread layout. We will connect these concepts with emerging hardware features and future demands on programming systems to reduce data movement.