The consideration of ensemble observability is, in particular, motivated by recent efforts in the study of heterogeneous cell populations. Therein one aims to reconstruct a distribution of states within a population of cells, but is only given the time evolution of the distribution of certain measured quantities within the population. More generally, the motivation for introducing ensemble observability is rooted in the very concept of ensembles itself, in which a collection of individual systems may only be considered as a whole. A main result of this thesis illustrates a fundamental connection between the concept of ensemble observability and mathematical tomography problems. Another main result concerns a natural connection to polynomial systems, which we encounter in the course of a systems theoretic treatment of the ensemble observability problem through the consideration of moments of the distributions. We also establish a duality of both approaches for linear systems.