||What is a Khalimsky manifold? The answer is not so obvious. We would like to call a topological space that is locally homeomorphic to Khalimsky n-space a Khalimsky n-manifold. We shall discuss several possible definitions and their consequences. If the requirements are too relaxed, then very strange spaces are allowed as manifolds. On the other hand, if the requirements are to strict then important spaces are excluded. As an example, we show that a seemingly natural attempt to define Khalimsky manifolds results in the non-existence of a Khalimsky sphere.