I'm a professor in the humanities so I can write tests that make it harder to cheat than some other fields. I cringe whenever I hear someone using these invasive kinds of software. There has to be a better way than making students install spyware.
Even so, based on what I've heard from my immediate superior, I'm flagging somewhere between 10-20% of all of the plagiarism and cheating cases in my faculty.
It's not hard to detect (generally good writing mixed with bad on essays / the repetition of similar phrases by different students on exams), but it does take a bit of time to confirm and you need to write a some policy-consistent boilerplate to make it simple to take action.
Some here have suggested that we need to write the equivalent of "open book" exams for the online environment. I'm not sure that would be beneficial. It's still important to exercise your mental faculties. People who can recall information and reason for themselves are still more valuable than those who can cut and paste. Or to put it another way, you need to understand the math in order to wield a calculator well.