Our ability to collect data is rapidly increasing thanks to computational power and the unprecedented diversity of sensors. But how good are we at extracting, reconstructing, and understanding information from them? Big data are not easy to digest. Our knowledge about the Earth system is not increasing at the same speed as data, but it follows the slower progress of Data Reconstruction and Modelling techniques. Performing in-silico experiments on ideal/complex systems, we examine the applicability of Physics-Informed Data-Driven (PIDD) tools to extract interpretable information from sparse & heterogeneous observations of complex flows. Key applications are data-driven physics modeling, data augmentation, and super-resolution. We compare state-of-the-art purely Data-Driven tools, such as Generative Adversarial Networks (GAN) [1], with purely Physics-Informed approaches, such as Nudging [2], on the ability to reconstruct missing data. At the same time, we will discuss how the potentials of both techniques are combined in the most advanced Physics-Informed Neural Networks. Moving from ideal cases such as turbulence on a rotating frame or Rayleigh-Benard convection I will discuss how PIDD tools can potentially result in a ground-breaking methodological revolution of today's data analysis and data-reconstruction techniques in applications such as ocean observations [3,4].