Cardio Training or Weight Training
For many years now it was been well understood that it's either one or the other. Meaning, if you place your emphasis on cardio work muscular development (or strength) will actually regress. And, if you place your emphasis on muscular strength development, your cardio improvements will regress.
This is not good news for most people that want to develop both, and that would include most people at the gym. If you simply want general health, both cardiovascular and muscular fitness is possible. But, if you want to become a marathon runner you simply won't be able to become a serious body builder. The good news is there is recent research that shines a bit more light on this area.
Which ever adaptation is most important to you is what you should do first during your workout. For example, if you are training for a summer that will involve a lot of running, during the spring you should run first, then do your strength training. And vica versa.
Apparently there is evidence that your body cannot switch from one to the other. Meaning, the switch that controls adaptations is the same switch for both, and once it's pushed to one setting it will stay there for that specific workout. So, if you start your workout with a jog on the treadmill your switch will be set to cardio gains. Even after the jog, while you are now doing weights, that switch will remain where it was originally, and cardio gains will dominate.
If you want both adaptation equally, switch things up. E.g. for two weeks do weights first, then for the next two weeks do cardio first. This is also a good way to keep your body guessing and to avoid plateau in physical gains.
Another approach is to alternate based on the season. For example, if you are a cyclist, during the winter you would put more emphasis on weight training with minimal cardio. Then, during the spring put your cardio work first, as you prepare for the summer cycling season.