I have yet to get the mesh deform modifier to do anyhting I tried on a character, with a complex mesh, nothing worked, so tried a new grid that was simpler from scratch, didn't work, now just a cylinder with Suzanne (supplied file) nothing. I checked to make sure scale =1 , location and rotation  are at zero and UV's are pointing out. 

The cylinder comes with a shape key to skew it.

I never got the modifier to work once. 
What am I doing wrong?
In your file everything would work exactly like it should my friend if you'd add mesh deform modifier to appropriate mesh :). You should add it to the mesh you want deform and as Object choose the mesh you want to deform with, so in this case modifier should go to Suzanne and the object should be Cylinder.