If you mean computer monitors, then it depends a lot on the monitor.
Two major things to consider:

1. If you want to output the sound through HDMI, the monitor will need Speakers or a sound output you can connect speakers to. Alternatively you have to get the sound out of the PS4 via other means (PS3 had an optical connector, dunno about the 4).

2. A computer scales the picture for the monitor usually, which is why some monitors have terrible input scaling. The Ps 4 probably doesn't scale and just outputs a 16:9 picture that the monitor has to scale itself. If the monitor is 16:9 and the PS4 outputs 16:9 there shouldn't be a problem. When I wanted to connect my PS3 to my 16:10 monitor though I researched this (back in 2008) and selected a monitor that wouldn't squeeze the picture or cut parts off left and right. Maybe not the biggest issue anymore with 16:9 nowadays. For 21:9 and other monitors this might still be problematic though if their internal scaling is terribly implemented.

Other than these two things, a computer monitor should be able to handle an HDMI input from a PlayStation just like a TV. My old one (24" Benq G2400W) certainly did it very well, haven't tried it on the new one so far as I don't play on the old PS3 anymore.