This work presents a comprehensive suite of data-driven strategies to advance the simulation, modeling, and control of both incompressible and compressible fluid flows. A novel adaptive mesh refinement (AMR) framework, powered by dominant balance analysis (DBA), dynamically allocates computational resources to regions of critical physical interaction, achieving significant cost reduction while preserving accuracy. To address transient instabilities, we introduce modeling tools that capture and manipulate the phase-amplitude dynamics of the flows. Additionally, new autoencoder-based strategies enable one-shot flow behavior prediction and facilitate model-free control of latent dynamics, offering a robust approach for efficient flow management.