The development of metallic alloys is arguably one of the oldest of sciences, dating back at least 3,000 years. It is therefore very surprising when a new class of metallic alloys is discovered. High Entropy Alloys (HEA) appear to be such a class furthermore, one that is receiving a great deal of attention in terms of the underlying physics responsible for their formation as well as unusual physical,mechanical and radiation resistance properties that make them candidates for technological applications. The term HEA typically refers to alloys that are comprised of 5, 6, 7… elements, each in in equal proportion, that condense onto simple underlying crystalline lattices but where the different atomic species are distributed randomly on the different sites -face centered cubic (fcc) Cr0.2Mn0.2Fe0.2Co0.2Ni0.2 and body-centered-cubic (bcc) V0.2Nb0.2Mo0.2Ta0.2W0.2 being textbook examples. The naming of these alloys originates from an early conjecture that these unusual systems are stabilized as disordered solid solutions alloys by the high entropy of mixing associated with the large number of components - a conjecture that has since proved insufficient. In the first part of the presentation I will describe a model that allows us to predict which combinations of N elements taken from the periodic table are most likely to yield a HEA that is based on the results of modern high-throughput ab initio electronic structure computations. In the second part I will broaden the discussion to a wider class of equiatomic fcc concentrated solid solution alloys that is based on the 3d- and 4d-transition metal elements Cr, Mn, Fe, Co, Ni, Pd that range from simple binary alloys, such as Ni0.5Co0.5 and Ni0.5Fe0.5, to the quinary high entropy alloys Cr0.2Mn0.2Fe0.2Co0.2Ni0.2 and Cr0.2Pd0.2Fe0.2Co0.2Ni0.2 themselves. Here I will discuss the role that increasing chemical complexity and disorder has on the underlying electronic structure and the magnetic and transport properties. Finally, I will argue that the manipulation of chemical complexity may offer a new design principle for more radiation tolerant structural materials for energy applications.