For a long time, LCD monitors weren't even up to the challenge. The technology just didn't allow the range of colors a CRT could produce. But these days that it isn't a problem.
Not every LCD screen will be color-accurate. There are actually several LCD screen technologies in use. Each one has strengths and weaknesses. I'll cover them briefly, but I won't go into the technical differences.
The most common LCD type is twisted nematic (TN). It is used in almost any screen you see in a store. That's because it's inexpensive and has fast response times.
That's good for the average computer user. However, TN's color accuracy and viewing angles aren't great. Professionals steer clear of TN technology for serious work.