The process of amending the U.S. Constitution, whether by Congress or Constitutional Convention, is described in Article V. 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?
A Constitutional Convention for the purpose of amending the Constitution may be called if two-thirds of state legislatures vote to apply for a Constitutional Convention. Currently, that would be 34 states (rounded up from 33.33).

Since the U.S. Constitution was signed in 1789, no Constitutional Convention has ever been held.

The Constitution does not specify what percentage of a state's legislature must be in favor of the application (simple majority in both houses? Two-thirds in both houses as is required when Congress generates an amendment?)

The Constitution does not specify who keeps track of the applications. For now, applications are read into the Congressional Record¹. Neither is it clear if all of the applications have to have the exact same wording.

Over the years, states have also rescinded their applications, even though it is not clear whether rescissions are valid. In practice, rescissions are also read into the Congressional Record.

The Constitution does not state who would be delegates to a Constitutional Convention, nor does it state how many delegates a state would send to such a convention. Possibly, a state would send as many delegates as it has representation in both houses of Congress. Perhaps the delegates would be the state's current elected representatives and senators.

It is not clear whether, once called, a Constitutional Convention can be restricted to a single topic or whether such a convention would be a free-for-all and able to consider and pass any number of amendments. In 1988, former Chief Justice of the United States Warren Burger wrote "[T]here is no way to effectively limit or muzzle the actions of a Constitutional Convention.²

The Constitution says that any amendments "shall be valid to all Intents and Purposes, as Part of this Constitution," when agreed to by "three fourths thereof, as the one or the other Mode of Ratification may be proposed by the Congress;".

This implies that Congress determines whether the Constitutional Convention delegates representing their respective states vote to ratify an amendment or whether proposed amendments are sent to the states for their legislatures to vote on. In either case, three-fourths of the states must vote in favor of an amendment in order for it to be considered ratified. Currently, three-fourths of the states is 38 states.

There is nothing to prevent a Constitutional Convention from changing that rule and reducing the number of states required to ratify an amendment ... say, for example, from three-fourths to two-thirds.²

The federal judiciary has no jurisdiction over a Constitutional Convention and cannot be called upon to settle disputes.²

According to the National Conference of State Legislatures⁴, for an amendment produced by Congress to be ratified by a state, both of a state's houses must ratify the amendment by an up-or-down vote, aka a simple majority. Presumably, the same rule would apply to amendments produced by a Constitutional Convention.

The Constitution does not state whether governors can veto a legislature's application for a Constitutional Convention or 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.⁴

The last clause, "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," forbids the ratification of amendments that would repeal the language in Article I, Section 9, which prohibits a ban on the importation of slaves prior to 1808, or the language in Article I, Section 3, which provides for equal representation of the states in the Senate.⁵

Where do we stand now?
The Republican's "Redmap" project brought the number of states in which Republicans control both houses of a state's leglislature dangerously close to the 34 states currently required to hold a Constitutional Convention.

After the 2018 election, these 30 states have Republican-controlled legislatures:³

Arizona	Utah	Wyoming	Georgia	North Dakota	South Dakota
Nebraska	Kansas	Oklahoma	Texas	Louisiana	Arkansas
Missouri	Iowa	Wisconsin	Tennessee	Mississippi	Alabama
Indiana	Michigan	Ohio	Pennsylvania	West Virginia	North Carolina
Florida	South Carolina	Kentucky	Idaho	Virginia	Montana

The 2018 results are an improvement over the 2016 numbers. As a result of the 2018 elections, New Hampshire, Colorado flipped to full Democratic control, and Alaska and Minnesota flipped to mixed control. Hopefully, these Demcratically-controlled houses know enough not to pass a Constitutional Convention application.

Several groups are currently advocating for holding an Article V Constitutional Convention.

Balanced Budget Amendment
The corporate lobbying group, American Legislative Exchange (ALEC), is a proponent of the Balanced Budget Amendment (BBA), which would force the federal government to run a balanced budget.³

Proponents of the BBA have gotten the closest to calling for a Constitutional Convention. After reaching a highpoint of 32 states in 1989, 12 states had rescinded their applications by 2010. By 2011 and with the support of Tea Party movement, many state legislatures had applied or reapplied for a Constitutional Convention.

As of March 2018, 28 states had active applications for a Constitutional Convention based on the BBA. The states are:

Arizona	Utah	Wyoming	Colorado	North Dakota	South Dakota
Nebraska	Kansas	Oklahoma	Texas	Louisiana	Arkansas
Missouri	Iowa	Wisconsin	Tennessee	Mississippi	Alabama
Indiana	Michigan	Ohio	Pennsylvania	New Hampshire	North Carolina
Georgia	West Virginia	Florida	Alaska

New Hampshire and Colorado flipped to a Democratic-controlled legislature, and they, presumably, will rescind their applications, but it is not clear that they have or will. Alaska's legislature switched to mixed, making Alaska unlikely to rescind its application. Minnesota, which had not filed a BBA-based application before 2018, switched to mixed, hopefully making it unlikely that it will file a BBA-based application.

As of March 2018, several states with Republican-controlled legislatures had not yet become Article V BBA applicants: Kentucky, Idaho, Montana, South Carolina and Virginia. If Colorado and New Hampshire rescind their applications and all of those five states apply, the tally would stand at 31 - just three states short of the 34-state goal. (Note that I need to research whether any of these states have applied in the past year.)

The Convention of States
Another Article V effort is called "The Convention of States," bankrolled by the Mercer family and the Koch-connected Donors Trust and supported by Senator Marco Rubio, former Arkansas Gov. Mike Huckabee, Texas Gov. Greg Abbott, Senator Rand Paul, former Florida Gov. Jeb Bush, Mark Levin, Sean Hannity, Pete Hegseth, Allen West, former Alaska Gov. Sarah Palin, Florida Gov. Ron DeSantis, ALEC, and others. The Convention of States is focused on limiting the powers of the federal government, imposing fiscal restraints on federal spending and applying term limits for members of Congress.³

As of March 2018, fifteen states have cited The Convention of States as their reason for applying for a Constitutional Convention:

Arizona	Utah	North Dakota	Alaska	Texas	Oklahoma
Missouri	Arkansas	Louisiana	Tennessee	Indiana	Florida
Mississippi	Alabama	Georgia

In 2016, proponents of "The Convention of States" held a mock Constitutional Convention, including participants from states that had NOT applied for such a convention. They proposed to adopt amendments that would "drastically alter the federal government and put civil rights and needed programs, including Social Security, Medicare, and Medicaid, at risk."³

The Wolf PAC
Since 2014, Vermont, California, New Jersey, Illinois and Rhode Island have applied for a Constitutional Convention to overturn Citizens United. This effort is led by political commentator Cenk Uygar working under the auspices of Wolf PAC.³

Final thoughts
"An Article V constitutional convention is a dangerous and uncontrollable process that would put Americans' constitutional rights up for grabs."³

The threat of a Constitutional Convention being held in these polarized, gerrymandered times should be enough to get Democrats off their duffs and make Washington D.C and Puerto Rico states ASAP. Doing so would increase the number of states required to apply for a Constitutional Convention from 34 to 35. It would shift the number of states required to approve an amendment to the Constitution from 38 to 39.