The VMO is short for vastus medialis oblique. It is the tear drop muscle on the inside portion of your leg. It has major implications in knee health. It is one of those muscles that seem to get amnesia whenever there is trauma around the joint. So if you have ever had a knee injury, chances are it's not as strong as you need it now to be. It has direct involvement in patellar femoral pain.
Research is finding new things about this interesting muscle. Recently they have discovered that the VMO has actually three motor innervation's while the other quadricep muscles, vastus intermedius, lateralis and rectus femoris only have one. There is good reason to believe that there is fascial connections to the actual patellar tendon an also into the adductor magnus. So you can see this muscle has influence in a lot of places!
So how to train it? I think the best way to train such an intricate muscle is to be varied. The VMO has been show to be around 52% type 1 muscle fibers. So it must also be trained for endurance, not just pure strength. For this I like a time under tension approach. One of my favorites is to pull a sled backwards in a low crouch position. Try pulling a heavy sled backwards for 60 seconds. You will feel your VMO's if you have never felt them before!
Terminal Knee Extensions or TKE's as they are known in the rehab world is another simple exercise. It involves something as simply as placing a theraband around something secure and then around your knee. Face in the direction of where the band is secured to. Bend the knee slightly under tension and contract your quad so that your leg straightens. I like this more for activation the strengthening. So if you have just had knee trauma this is one of the better ones to start with.
Step ups on a slight decline is another great exercise. On a medium to low box ( 8 to 12 inches) that is slightly declined. Place your foot facing going down the step. With an erect posture dip and straighten the leg.
Single leg activities that require balance checks such as a single leg dumbell deadlift will challenge the proprioception and stability of the VMO.
Finally any full squat will develop the strength qualities of the VMO. Check any Olympic lifters VMO and they are highly developed. Snatch Grip Deadlifts off a podium of 2-4 inches is my favorite all around exercise and will develop the VMO as well.
So hope this helps you with exercise selection when thinking about targeting the VMO. Remember that variety is the key to a well developed functional muscle.