H-1B holders can seek green cards through a variety of ways: green card lottery (for certain countries), family sponsorship (such as marriage green cards), and employment sponsorship (the EB-1, EB-2, EB-3, EB-4, and EB-5 categories.)

Within the EB's, most companies will sponsor H-1B holders for green cards in the EB-2 or EB-3 categories in a 3-step process: PERM, I-140, I-485.

If an H-1B holder wants to get a green card based on work/accomplishments as a self-petitioner, the two main pathways are:

Eb-1A for extraordinary ability, helpful for people subject to long India/China backlogs

Eb-2 NIW, easier than O-1A, takes 2-3 years if you're not subject to India/China backlogs.