H-1B visa holders can bring their spouse and unmarried children under the age 21 years of age to the U.S. under the H-4 non-immigrant visa program. H-4 visa holders are allowed to study and generally are not eligible to work in the U.S, but some may be entitled to a work authorization.
An H-4 visa holder is allowed to remain in the U.S. as long as the H-1B visa holder has a valid legal status.