I know that there are varieties of surgeries to treat cataract. What are they?

Cataract surgery. The most common type of cataract surgery, called phacoemulsification, uses ultrasound to break up the cataract into tiny pieces, which are then aspirated from the eye. The latest cataract removal technique is called femto cataract surgery, which uses a laser to break up the cataract. This is only available in a few cities, and is rapidly gaining popularity.
Limited options. Cataract removal has evolved to in most cases the use of the highly successful phacoemulsification method. Most other surgeries for almost all cataracts are more risky. There are choices of lenses to be inserted and the power of the lenses to meet various personal needs. You can discuss these options with the surgeon you select to remove your cataract.
Laser Cataract Surg. New intraocular implants (IOL) & advanced technology now exist for Cataract Surgery. IOLs: multifocal lens, accommodating lens, toric for astigmatism; For CS: can be done with LASER: femtosecond laser or tradition Clear cornea (with blade), Scleral tunnel, Extracap (rarely used); ORA: intraoperative aberrometry also used to help get best IOL implanted. More info: eyedoc2020@blogspot.com.
Really just two. Most people in the US have phacoemulsification using ultrasound to remove cataract. There is also extracapsular cataract extraction where the cataract in removed manually, used in the US usually when the cataract is too fragile or hard to remove with ultrasound. Femtosecond laser is used in cataract surgery as an addition to the phacoemulsification surgery, that has only recently been approved.