Like many of you, I'm not a big cardio person. I truly enjoy strength training, whereas cardio is that tedious bit of my workout I feel compelled to "get out of the way" before I can get to my weight-training session. So, like many of you, I generally do my cardio workout (25-30 minutes) before I do my lifting (30-35 minutes).
A question we trainers are frequently asked is whether it's better to do cardio before or after weights. Though the answer can be invariably complex---and depend on the client's goals---historically I've given what, to me, is a common-sense answer: Do the thing you're least likely to do first. That is, if motivation is an issue, and you know that you won't stick around for another half hour to use the elliptical after an intense weight workout, or you won't put as much energy into it, it might be a better idea to get the cardio out of the way first.
This response, I've decided, is a bit of a cop-out. It implies that cardio is nothing but a throwaway aspect of your workout, or that one is more valuable than the other. And while the industry has long been divided over the correct response to the cardio-before-weights question, more recent studies are showing a benefit both in muscle hypertrophy and fat loss to doing your resistance training first. Several high-profile trainers like Tony Hale and Jillian Michaels are in this camp.
Here's their explanation: During exercise, our bodies burn fuel in this order---glycogen (stored carbohydrates in muscle and liver tissue) first, then fat stores. Though opinions differ here, it can take up to 30 minutes for the body to burn through its glycogen. The idea, then, is that if you do 30 minutes of cardio, you'll have depleted the energy your muscles require for strength training (which is anaerobic and depends on glycogen), as well as forfeited your opportunity to burn your fat stores during cardio. However, if you weight train first, you'll burn up your glycogen, leaving your body free to burn fat during cardio. Here and here you'll find articles further explaining this theory.
On the other hand, many trainers and exercise physiologists dismiss the "fat-burning zone" as myth. They argue that doing a moderate 30-40 minutes of cardio doesn't come close to burning up the glycogen you need to get through a weight workout (provided you get the proper nutrition before your workout), and that fat burn has more to do with total calories expended than anything else. Here and here are articles expounding on this argument.
So what's the right answer? First, consider your goals. Whether you're working out for weight loss, increased muscle mass, or strength gain plus fat loss, we know this much: it's a good idea to fit both cardio and strength into every workout. A move away from the old thinking that you had to do five cardio sessions per week and only a couple of strength workouts, this is advice that many fitness experts do agree upon.
Now, if endurance training is your main objective, like training for a marathon, then you want to put the bulk of your energy expenditure into cardio training and should put that first. Likewise, if you're a competitive bodybuilder or just trying to achieve bulk, putting weights first is advisable. For everyone else: I would suggest giving both methods a try. Everyone's body is different; therefore it's hard to predict that the same technique will work equally well for all people. If, like me, you tend to do cardio first, switch it up for a month and see if you get better or renewed results. At the very least, you'll be breaking from routine.