Captchas are not outdated. They are good against brute-forcing password for example: 10 unsuccessful login attempts -> please use captcha. Since brute-forcing takes millions or tens of millions of attempts, it becomes uneconomical.
Another method is to pause for an exponential delay after each failed attempt. This makes it prohibitively slow to brute force.
The benefit of the captcha method is that your account can't be DOSed -- the legitimate user can still get in by entering one captcha, which is much better than, say, having to wait for an hour.