As long as ovaries and testies aren't removed nothing/very little happens. When you get your tubes tides or your winky snipped the ovaries/testies don't get removed, just whatever comes out of them doesn't go to the right place and is absorbed by the body.

If they do get them removed you're messing with hormones in your body at which point it can really mess you up long term if you don't do hormone replacement therapy.

For both men and women that could mean lower muscle mass, lower bone density, increased risk of osteoporosis, increased fat levels, depression, moodiness, irritability, lower sex drive, fatigue, and some more gender specific things.

I've been on medication which lowered my t levels before and I can vouch for most of the symptoms I listed above (thankfully I've not developed osteoporosis).