There are now three license classes: Technician, General and Amateur Extra. You begin by passing a written exam for the Technician license, then you must pass an additional exam for General and one for Extra. No more code tests. The exams are multiple choice and are roughly half rules and half technical information.

The Technician license is primarily limited to FM voice on VHF/UHF (above 30 MHz). If you see a ham talking on a HT (walkie-talkie) or a mobile radio, they are probably on VHF/UHF FM. You can do code (and many other non-FM modes) on those available bands, but it's not trivial for the beginner. Many experienced hams enjoy working those bands and modes though.

The General license opens up almost all of the HF (shortwave) bands or what people traditionally think of when they talk about ham radio. Big antennas, towers, talking around the world, etc. Code is definately still around and some new hams continue to learn it.

The Extra license only really adds some extra frequencies on each band to what the General license has.