Didymium (Greek: δίδυμο, romanized: dídymo, twin) is a mixture of the elements praseodymium and neodymium. It is used in safety glasses for glassblowing and blacksmithing and filter lenses for flame testing, especially with a gas (propane)-powered forge, where it provides a filter that selectively blocks the yellowish light at 589 nm emitted by the hot sodium in the glass without having a detrimental effect on general vision, unlike dark welder's glasses and cobalt glasses. The usefulness of didymium glass for eye protection of this sort was discovered by Sir William Crookes.

Didymium photographic filters are often used to enhance autumn scenery by making leaves appear more vibrant. It does this by removing part of the orange region of the color spectrum, acting as an optical band-stop filter. Unfiltered, this group of colors tends to make certain elements of a picture appear "muddy". These photographic filters are also used by nightscape photographers, as they absorb part of the light pollution caused by sodium street lights. Didymium was also used in the sodium vapor process for matte work due to its ability to absorb the yellow color produced by its eponymous sodium lighting.

Didymium is also used in calibration materials for spectroscopy.

Didymium was discovered by Carl Mosander in 1841. It was named after the Greek word δίδυμο ("twin") because it is very similar to lanthanum and cerium, with which it was found. Mosander wrongly believed didymium to be an element and that cerite, isolated by Jöns Jakob Berzelius in 1803, was a mixture of cerium, lanthanum, and didymium.^{[citation needed]} Cerium, lanthanum, and didymium made up at least 95% of the rare earths in the original cerite from Bastnäs, Sweden.

In trivalent form, didymium tinged the salts of ceria pink. During the time that didymium was believed to be an element, the symbol Di was used for it. In Dmitri Mendeleev's first attempt at a periodic table, the atomic weights assigned to the lanthanides (including didymium) reflect the original belief that they were divalent. Their actual oxidation number of 3 implies that Mendeleev underestimated atomic weights for them by one third.

In 1874, Per Teodor Cleve deduced that didymium was made up of at least two elements. In 1879, Lecoq de Boisbaudran succeeded in isolating a samarium compound for the first time; the compound was isolated from didymium contained in North Carolinian samarskite. In 1885, Carl Auer von Welsbach succeeded in separating salts of the last two component elements, praseodymium and neodymium. To accomplish this, he used a fractional crystallization of the double ammonium nitrates from a solution of nitric acid.

Welsbach had decided to name his two new elements "praseodidymium" ("green didymium") and "neodidymium" ("new didymium"), but one syllable was soon dropped from each name. Despite being abbreviated in the new elements' names, the untruncated name "didymium" persisted, partly due to its use as an ingredient in glassblowers' goggles, and colored glass. The name "didymium" also was retained in mineralogical texts.

During World War I, didymium mirrors were reportedly used to transmit Morse Code across battlefields. Didymium does not absorb enough light to make the variation in lamp's light output obvious, but someone with binoculars attached to a prism in the correct fashion could see the absorption bands flash on and off.