The simple connection between the Slater orbitals, venerable in quantum chemistry, and the Coulomb Sturmian orbitals, more recently employed in atomic and molecular physics, is pointed out explicitly in view of the renewed interest in both as basis sets in applied quantum mechanics. Research in Slater orbitals mainly concerns multicentre, many-body integrals, whereas that on Sturmians exploits their orthonormality and completeness with no need of continuum states. An account of recent progress is outlined, also with reference to relationships between the two basis sets, and with the momentum space and hyperspherical harmonics representations. The connection between the venerable Slater orbitals in quantum chemistry and the Coulomb Sturmain orbitals is pointed. An account of recent progress is outlined with reference to their relationships with the momentum space and hyperspherical harmonics representations.