Many elemental metals become superconductors at sufficiently low temperatures, but not all. Ironically, some of the normal metal elements with the best electrical conductivity (gold, silver, copper) do not appear to do so. Conventional superconductivity was explained by Bardeen, Cooper, and Schrieffer in 1957. Oversimplifying, the idea is that electrons can interact with lattice vibrations (phonons), in such a way that there is a slight attractive interaction between the electrons. Imagine a billiard ball rolling on a foam mattress - the ball leaves trailing behind it a deformation of the mattress that takes some finite time to rebound, and another nearby ball is "attracted" to the deformation left behind. This slight attraction is enough to cause pairing between charge carriers in the metal, and those pairs can then "condense" into a macroscopic quantum state with the superconducting properties we know. The coinage metals apparently have comparatively weak electron-phonon coupling, and can't quite get enough attractive interaction to go superconducting.
Another way you could fail to get conventional BCS superconductivity would be just to have too few charge carriers! In my ball-on-mattress analogy, if the rolling balls are very dilute, then pair formation doesn't really happen, because by the time the next ball rolls by where a previous ball had passed, the deformation is long since healed. This is one reason why superconductivity usually doesn't happen in doped semiconductors.
Superconductivity with really dilute carriers is weird, and that's why the result published recently here by researchers at the Tata Institute is exciting. They were working bismuth, which is a semimetal in its usual crystal structure, meaning that it has both electrons and holes running around (see here for technical detail), and has a very low concentration of charge carriers, something like 1017/cm3, meaning that the typical distance between carriers is on the order of 30 nm. That's very far, so conventional BCS superconductivity isn't likely to work here. However, at about 500 microKelvin (!), the experimenters see (via magnetic susceptibility and the Meissner effect) that single crystals of Bi go superconducting. Very neat.
They achieve these temperatures through a combination of a dilution refrigerator (possible because of the physics discussed here) and nuclear demagnetization cooling of copper, which is attached to a silver heatlink that contains the Bi crystals. This is old-school ultralow temperature physics, where they end up with several kg of copper getting as low as 100 microKelvin. Sure, this particular result is very far from any practical application, but the point is that this work shows that there likely is some other pairing mechanism that can give superconductivity with very dilute carriers, and that could be important down the line.