Note: Everything mentioned in my blog is based on evidence-based research studies. I have no professional experience and don't claim any of the medical suggestions as my own. My attempt is merely to compile, explain, and present the findings of researchers in a manner that helps my readers implement lifestyle changes that improve their health. I strongly believe in and practice what I write about; these have helped me, and I hope they help you as well.
The most time-efficient method to get all the benefits of aerobic exercise is high-intensity interval training (HIIT).
HIIT actively combats insulin resistance 
Increases growth hormone by 2,000% 
And it “elicits metabolic adaptations that resemble traditional high-volume endurance training (ET)” 
Mark Sisson, a New York Times bestselling author, former endurance runner, triathlete, and Ironman competitor who now advocates HIIT instead of chronic cardio, said it well: “the popular wisdom of the past 40 years – that we'd all be better off doing 45 minutes to an hour a day of intense aerobic activity – has created a generation of overtrained, underfit, immune-compromised exerholics.” 
Endurance athletes are at increased risk of cardiac arrythmias as well as atrial fibrillation (AF) . AF “raises the risk of stroke, heart failure, blood clots and other cardiovascular complications.” 
Marathon runners also have more calcified plaque in their coronary arteries  which has been linked to stroke and dementia.
If you're one of those who enjoys distance running, then by all means go for it! I reduced endurance training about a year ago and now do HIIT and recommend it as the main method that you perform your aerobic exercise.
HIIT is described as “a cardiovascular exercise strategy alternating short periods of intense exercise with less intense recovery periods.”
One can use any full-body demanding movement for the exercise, such as swimming, running, cycling, elliptical machine, or the likes of jumping jacks, burpees, skipping etc.
Three examples of great HIIT workouts are:
Long Interval HIIT
3-4 minutes at a hard exercise with
3-4 minutes active recovery,
repeated for 24-32 minutes
Short Interval HIIT
30 seconds intense exercise with 30 seconds recovery,
repeated for 10-15 miuntes
20 seconds of ultra-intense exercise with 10 seconds of rest,
repeated for 4 minutes (8 rounds)
“Athletes using this method trained 4 times per week for 4 minutes for 6 weeks and obtained gains similar to a group of athletes who did 60 minutes steady state training 5 times per week.” 
If you enjoy music while exercising you could check out Tabata Songs.
Using appropriate movements:
When using a treadmill one can run at a high pace for 3-4 minutes for long interval HIIT. However, a treadmill is not practical to run at an intense pace in 20-30 seconds spurts, as is required for short interval HIIT or Tabata. To achieve those intense spurts I use an Elliptical.
Another popular and efficient method is
high-intensity circuit training (HICT).
A seven minute HICT workout was created by the American College of Sports Medicine  to help obtain the benefits of exercise in less time. It consists of 12 aerobic and resistance exercises of all the major muscle groups. Each exercise is performed for 30 seconds at an intensity of 8-10 (on a scale of 1-10), with a rest of 10 seconds in between exercises. In total, this adds up to 7 minutes.
The image is a resource for workouts with different intensities, Zone 1 being the lowest intensity while Zone 5 the highest one. The third column shows a few example sessions for each Zone.
I recommend that you work in Zone 5, which correlates with HIIT, to get more efficient exercise.
Want to learn more?