Information Theory provides a fundamental basis for analysis, and for a variety of subsequent methodological approaches, in relation to uncertainty quantification. The transversal character of concepts and derived results justifies its omnipresence in scientific research, in almost every area of knowledge, particularly in Physics, Communications, Geosciences, Life Sciences, etc. Information-theoretic aspects underlie modern developments on complexity and risk. A proper use and exploitation of structural characteristics inherent to spatial data motivates, according to the purpose, special considerations in this context. In this paper, some of the most relevant approaches introduced, in particular recent contributions and directions, regarding the informational analysis of spatial data and related aspects concerning complexity analysis, are reviewed under a conceptually connective evolutionary perspective. The discussion involves the cases of spatial data from magnitude measurements and spatial point patterns, with the latter possibly being of a multifractal nature.