We review recent developments related to inferencefor functions defined at spatial locations. We also considertime series of functions defined at irregularly distributedspatial points or on a grid. We focus on kriging, estimationof the functional mean and principal components, and significancetesting, giving special attention to testing spatio--temporalseparability in the context of functional data. We also highlightsome ideas related to extreme value theory for spatially indexed functionaltime series.
