I went through this about a year ago.
There are multi-focal lenses and accommodating lenses. The multi-focal jobs bring a lot of compromise with them and are, in my opinion, the least preferable solution. The accommodating lenses allow the muscles in your eye to change the shape of the soft lens implant and thus mimic a natural eye's function. The knock on the accommodating lenses is that the range of focal length that they deliver from patient to patient is highly variable, but I've not heard anyone say they flat out don't work.
In my case I let the ophthalmologist talk me out of an accommodating lens, then he missed the calculations and overcorrected. I might have been able to salvage a bit more usable vision with an accommodating lens. Water under the bridge now.
