Modern operating systems understand Unicode internally, but font support for Unicode is spotty. For an example of the problems this can cause, take a look at these screen shots of how the same Twitter message appears differently depending on what program is used to read it.
No font can display all Unicode characters. According to Wikipedia
… it would be impossible to create such a font in any common font format, as Unicode includes over 100,000 characters, while no widely-used font format supports more than 65,535 glyphs.
However, the biggest problem isn’t the number of characters a font can display. Most Unicode characters are quite rare. About 30,000 characters are enough to display the vast majority of characters in use in all the world’s languages as well as a generous selection of symbols. However Unicode fonts vary greatly in their support even for the more commonly used ranges of characters. See this comparison chart. The only range completely covered by all Unicode fonts in the chart is the 128 characters of Latin Extended-A.
Unifont supports all printable characters in the basic multilingual plane, characters U+0000 through U+FFFF. This includes the 30,000 characters mentioned above plus many more. Unifont isn’t pretty, but it’s complete. As far as I know, it’s the only font that covers the characters below U+FFFF.