AbstractA large variety of periodic tables of the chemical elements have been proposed. It was Mendeleev who proposed a periodic table based on the extensive periodic law and predicted a number of unknown elements at that time. The periodic table currently used worldwide is of a long form pioneered by Werner in 1905. As the first topic, we describe the work of Pfeiffer (Naturwiss. 8:984–991, 1920), who refined Werner’s work and rearranged the rare-earth elements in a separate table below the main table for convenience. Today’s widely used periodic table essentially inherits Pfeiffer’s arrangements. Although long-form tables more precisely represent electron orbitals around a nucleus, they lose some of the features of Mendeleev’s short-form table to express similarities of chemical properties of elements when forming compounds. As the second topic, we compare various three-dimensional (3D) helical periodic tables that resolve some of the shortcomings of the long-form periodic tables in this respect. In particular, we explain how the 3D periodic table “Elementouch” (Maeno in Periodic-table-of-the-elements stationery. Design No. 1149493, Japan Patent Office. https://www.j-platpat.inpit.go.jp/d0000, 2001), which combines the s- and p-blocks into one tube, can recover features of Mendeleev’s periodic law. Finally we introduce a topic on the recently proposed nuclear periodic table based on the proton magic numbers (Hagino and Maeno in Found Chem 22:267–273, 2020). Here, the nuclear shell structure leads to a new arrangement of the elements with the proton magic-number nuclei treated like noble-gas atoms. We show that the resulting alignments of the elements in both the atomic and nuclear periodic tables are common over about two thirds of the tables because of a fortuitous coincidence in their magic numbers.