How is CVT transmission in the Elantra different from automatics?

Like many modern compact cars, the Hyundai Elantra is sold with a CVT (Continuously Variable Transmission) in most of its models. Hyundai calls their Intelligent Variable Transmission (IVT). CVTs are praised for their smooth operation and better fuel economy, but they've also been panned for their 'rubber band' feel and possible reliability problems. Some drivers unfamiliar with traditional automatics find the CVT’s behavior unusual or unpleasant. Seamless acceleration and improved MPG is earned by others. The long term durability of CVTs is also debated against conventional automatics. While Hyundai says their IVT is a solution to many of the typical CVT gripes, owner and critics alike seem to have a wide array of opinions.