Injuries and fitness is now more or less implemented in the game (subject to bugs and changes in probability). I do have one more thing to include in terms of injury, and that is if you get injured during the course of a match.
Currently, you can get injured from training too hard. Your injury depends on the intensity of your training and what your fitness level was while you were training. You are injured for a certain number of matches. Each match your team plays, this number will come down. In the worst case scenario, you get injured for 20 matches (if your fitness level is 0 and your intensity of training is 100). However, if you continue to train, these days will add up.
So, in conclusion, you have to "take it easy" for a few days after getting injured and do simple exercises at a lazy intensity and build up your fitness again. Hence, when match time rolls around, you're ready to go.
You also lose fitness from playing games; in this sense, fitness is not so much literally fitness, but sort of a measure of stamina/general healthiness.