  When attempting to recover functions from observational data, one naturally
seeks to do so in an optimal manner with respect to some modeling assumption.
With a focus put on the worst-case setting, this is the standard goal of
Optimal Recovery. The distinctive twists here are the consideration of
inaccurate data through some boundedness models and the emphasis on
computational realizability. Several scenarios are unraveled through the
efficient constructions of optimal recovery maps: local optimality under
linearly or semidefinitely describable models, global optimality for the
estimation of linear functionals under approximability models, and global
near-optimality under approximability models in the space of continuous
functions.
