In recent years the fluid mechanics community has been intensely focused on pursuing solutions to its long-standing open problems by exploiting the new machine learning (ML) approaches. The exchange between ML and fluid mechanics is bringing important paybacks in both directions. The first is benefiting from new physics-inspired ML methods and a scientific playground to perform quantitative benchmarks, whilst the latter has been open to a large set of new tools inherently well suited to deal with big data, flexible in scope, and capable of revealing unknown correlations. A special case is the problem of modeling missing information of partially observable systems. The aim of this paper is to review some of the ML algorithms that are playing an important role in the current developments in this field, to uncover potential avenues, and to discuss the open challenges for applications to fluid mechanics.