The V visa is a temporary visa available to spouses and minor children (unmarried, under 21) of U.S. lawful permanent residents (LPR, also known as green card holders). It allows permanent residents to achieve family unity with their spouses and children while the immigration process takes its course. It was created by the Legal Immigration Family Equity Act of 2000 (LIFE Act). The Act is to relieve those who applied for immigrant visas on or before December 21, 2000. Practically, the V visa is currently not available to most of spouses and minor children of LPRs.

A permanent resident is a person who has been granted the right to reside permanently in the U.S. He/She is authorized to work and gains the right to become a U.S. citizen if he/she meets certain criteria.
The permanent resident is known as the sponsor of the immigrant visa petition while the spouse/child is known as the beneficiary.

A permanent resident who marries after getting his/her green card needs to file a Form I-130 (Petition for Alien Relative) with the USCIS. Once the I-130 is approved, the beneficiary needs to wait for an F2A immigrant visa. The F2A immigrant visa is heavily backlogged because only around 90K visas are available each year and demand exceeds supply. The current processing delays for the I-130 can be viewed at the USCIS website. The current backlog for F2A visas is updated each month. The date is available in the Visa Bulletin available from the State Department. U.S. family immigration is described in detail here.

While waiting for the I-130 to be approved or the F2A visa to become available, the beneficiary may visit the U.S. on B-2 visa (maximum 90 or 180 days stay) or under the Visa Waiver Program (VWP, maximum 90 days stay). However, in many cases, application for the B-2 visa or entry under the VWP is denied. Even once allowed a short-visit to the U.S., it cannot be repeated many times. Basically, the beneficiary cannot live or study in the U.S. This is because the visitor and student visas (or the VWP) require demonstration of non-immigrant intent. By definition, the spouse/child of a permanent resident cannot demonstrate non-immigrant intent.

The permanent resident, on the other hand, cannot be away from the U.S. for long periods. Doing so can be considered abandonment of permanent resident status.

This situation often separates the permanent resident from his/her spouse/child. These days, it takes 5-6 years before family unity can be achieved.