The process of amending the U.S. Constitution, whether by Congress or Constitutional Convention, is described in Article V of the U.S. Constitution. Here is the exact text, with the phrases pertaining to Constitutional Conventions highlighted in bold:

"The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution, or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which, in either Case, shall be valid to all Intents and Purposes, as Part of this Constitution, when ratified by the Legislatures of three fourths of the several States, or by Conventions in three fourths thereof, as the one or the other Mode of Ratification may be proposed by the Congress; Provided that no Amendment which may be made prior to the Year One thousand eight hundred and eight shall in any Manner affect the first and fourth Clauses in the Ninth Section of the first Article; and that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate."

What does it mean?
The Constitution can be amended when both houses of Congress, by a two-thirds majority, agree on the wording of a proposed amendment. Once Congress agrees on the wording of a proposed amendment, it is sent to the states for ratification. Three-quarters of the states have to approve the amendment for it to be considered "ratified" and part of the Constitution.

Given the current number of 50 states, 38 states would have to ratify an amendment before it is considered a part of the Constitution.

There have been approximately 11,700 attempts to amend the Constitution since it was signed in 1789. Of those, 27 efforts were successful. The first 10 amendments, known as the Bill of Rights, were ratified together in 1791.¹

The Constitution does not specify what percentage of a state's legislature must be in favor of a proposed amendment for the state to have considered to have ratified it. According to the National Conference of State Legislatures², to be ratified by a state, both houses must ratify the amendment by an up-or-down vote, aka a simple majority. (Note that of the 50 states, 49 states have a bicameral legislature. Only Nebraska has a unicameral legislature.)

The Constitution does not specify who keeps track of proposed amendments. Instead, 1 U.S.C § 106b.[4] charges the Archivist of the United States with administering the ratification process. When an amendment is property ratified by the requisite number of states, the archivist issues a certificate proclaiming that an amendment has become an operative part of the Constitution.¹

Over the years, states have also rescinded their ratification of an amendment, even though it is not clear whether rescissions are valid.

The Constitution does not state whether governors can veto a legislature's ratification of an amendment. According to the National Conference of State Legislatures, a governor's signature on a ratification bill is not necessary.²

The Constitution does not require proposed amendments to have a time-limit once they are given over to the states for ratification. There was no time-limit on early amendments. For example, the 27th amendment preventing Congress from receiving an increased salary until after the next election, was submitted along with the Bill of Rights on Sept. 25, 1789 but not ratified by enough states until 1992 - a period of over 200 years.

In more recent practice, time-limits have been included in proposed amendments.²

The Equal Rights Amendment
The Equal Rights Amendment was passed by both houses of Congress on March 22, 1972, sent to the states with a ten-year time limit and quickly ratified by 35 states. Then it fell victim to anti-abortion activists who argued that the ERA would interfere with their efforts to eliminate abortion. These states rescinded their ratifications: Nebraska, Tennessee, Idaho, Kentucky and South Carolina.

The Constitution does not mention rescissions, so a court battle will likely ensue if the requisite number of 38 states is ever met.

Possibly in response to the election of Donald J. Trump, Nevada ratified the ERA on March 21, 2017, and Illinois ratified the ERA on May 30, 2018.

If rescissions are ignored, the ERA is one state away from being ratified.

There were high hopes that with a near Democratic take-over of the Virgina governorship and Assembly, Virginia would approve the ERA in 2019. But on Feb. 19, Republicans defeated Democrats efforts in the Virginia House of Delegates to get the ERA out of committee by one vote.³

There were also hopes for the ERA in Arizona, but on March 15, 2019, Arizona Republican senators blocked a Democratic effort to get the bill out of committee for a full floor vote.⁴

Alaska	California	Colorado	Connecticut
Delaware	Hawaii	Illinois	Indiana
Iowa	Kansas	Kentucky*	Maine
Maryland	Massachusetts	Michigan	Minnesota
Montana	Nebraska*	Nevada	New Hampshire
New Jersy	New Mexico	New York	North Dakota
Ohio	Oregon	Pennsylvania	Rhode Island
South Dakota*	Tennessee*	Texas	Vermont
Washington	West Virginia	Wisconsin	Wyoming
Idaho*

^*Ratifications rescinded.

These states have never ratified the ERA: Alabama, Missouri, Arkansas, Arizona, North Carolina, Florida, Georgia, Oklahoma, South Carolina, Louisiana, Utah, Virginia and Mississippi.