The chemical elements are the “conserved principles” or “kernels” of chemistry that are retained when substances are altered. Comprehensive overviews of the chemistry of the elements and their compounds are needed in chemical science. To this end, a graphical display of the chemical properties of the elements, in the form of a Periodic Table, is the helpful tool. Such tables have been designed with the aim of either classifying real chemical substances or emphasizing formal and aesthetic concepts. Simplified, artistic, or economic tables are relevant to educational and cultural fields, while practicing chemists profit more from “chemical tables of chemical elements.” Such tables should incorporate four aspects: (i) typical valence electron configurations of bonded atoms in chemical compounds (instead of the common but chemically atypical ground states of free atoms in physical vacuum); (ii) at least three basic chemical properties (valence number, size, and energy of the valence shells), their joint variation across the elements showing principal and secondary periodicity; (iii) elements in which the (sp)8, (d)10, and (f)14 valence shells become closed and inert under ambient chemical conditions, thereby determining the “fix-points” of chemical periodicity; (iv) peculiar elements at the top and at the bottom of the Periodic Table. While it is essential that Periodic Tables display important trends in element chemistry we need to keep our eyes open for unexpected chemical behavior in ambient, near ambient, or unusual conditions. The combination of experimental data and theoretical insight supports a more nuanced understanding of complex periodic trends and non-periodic phenomena.