One way is to put a bunch of 74HC595 shift registers in series.
Another way is to use a microcontroller on both sides. uC's are a bit more expensive then shift registers, but you only need one of them, and you can combine it with scanning a matrix of LEDS, combine it with buttons, maybe a HD44780 or other stuff that's common on a front panel.
Then, there are all kinds of dedicated LED drivers. One of them is the MAX7219, which is a chip I do NOT like much. The "Maxim" variant is redicilously expensive, the clones from china are ... unreliable at best, and on top of that, the "dimmng" feature has far to few steps to be useful. On the plus side, this chip can handle a matrix of 8*8 = 64 LED's A lot of the bigger shops have whole separate sections for LED drivers.