Abstract: The recently emerging multi-principal element alloys (MPEAs) are attracting widespread attention. This naturally raises a materials science question as to what is new in the microstructure of these “high-entropy” alloys (HEAs) that makes them different from well-documented traditional (dilute) solid solutions. Here we illustrate that the concentrated chemical make-up towards equi-molar compositions in these multi-principal element solid solutions MPEA brings forth an unusually high population density of chemical inhomogeneities at length scales from sub-nanometers to a few nanometers. Specifically, a spatial variation in local composition, and in local chemical order (LCO), constitutes an inherent structural feature. In this article we define these various inhomogeneities and discuss the challenges facing their identification while explaining their relations with, and (sometimes subtle) differences from, the previously known inhomogeneities including the compositional coring in cast ingots, chemical short-range order and (precursor of) precipitates in conventional solid solutions. The potential impact is discussed in an outlook at the end, to provide a future perspective on this sub-field.