I have a CVT transmission, nothing fancy just means I buy Japanese cars, yea always have.
You feel how much smoother the ride is, SMOOTH ... More fuel efficient, yes, but not dramatic, however for a standard gas powered engine if you look at the years before CVT and after for the model, published fuel efficiency went up. I looked before buying. But if you want big gains in fuel efficiency it's not in this, it's in hybrids obviously, electric cars, maybe hydrogen cars (ha only CA has fueling stations for hydrogen cars at all). There is no replacing the timing belt on CVT I believe.