We mentioned the precious metals, which are a loose association of elements that are metallic, non-radioactive, useful, expensive, and rare. They generally occupy an area of the transition metals on the periodic table. Location in the periodic table has to do with the numbers of protons and electrons that make up an atom, and elements near each other have similar physical and chemical properties.
Silver and gold fall in the same group (column) as copper, which is Group 11 in the new system (and Group IB in the system most of the Clear Science staff grew up with). Sometimes these are called the coinage metals.
Ruthenium, rhodium, palladium, osmium, iridium, and platinum are collectively called the platinum group. This corresponds to Groups 8, 9 and 10 (or VIIIB).
Occasionally you hear some of these metals called "noble metals" because they are unreactive and resistant to most chemicals. Aqua regia ("royal water") was so named because it can dissolve platinum and gold, which is a difficult task indeed.