The crystals all have transition metals in them, which cause the colours. For example, if you dissolve copper sulfate in water it goes blue. This is because the way the electrons in the atom are arranged around the nucleus some are very close in energy. These electrons can absorb light in the visible spectrum and make the electrons jump to a higher energy. This absorbed energy means that we see them as being coloured.
Some other elements have colour, like liquid oxygen is pale blue, fluorine is green, but it is the chemistry of the transition metals that really is very very colourful, nearly all of them are coloured!
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