It was made public on Tuesday morning that the State of Texas filed a lawsuit late Monday evening in the Supreme Court of the United States suing the states of Georgia, Wisconsin, Michigan, and Pennsylvania for violating the U.S. Constitution, as well as their own constitutions.
Utilizing Article III Section 2 of the U.S. Constitution, Texas approached the Supreme Court directly. The Article provides that the judicial power extends to a dispute between two or more states. The Court doesn't necessarily have to take the case, but it without a doubt should.
The State of Texas is firstly arguing that the above-listed states violated the Electors Clause of the Constitution as they changed their voting procedures through courts and executive action, rather than through their legislatures, as required.
Texas is secondly arguing that voting rules varied county by county within the states, ultimately violating the Equal Protection Clause of the Constitution. This particular argument was at the forefront of the infamous Bush v. Gore Florida recount case in 2000 that went through the Supreme Court, ultimately ruled in favor of President Bush
Lastly, Texas is arguing that voting irregularities existed in the states being sued as a result of the first two above-mentioned items.
Bottom line, Texas is asking the Supreme Court to force the states to allow the legislatures appoint their electors - not the governors nor county officials. This is the intent of the applicable clauses of the Constitution and they should be upheld.
Along the lines of this case, Senator Ted Cruz (R-TX) offered to argue a Pennsylvania election case, should the Supreme Court of the United States agree to hear it.
Here's the documents filed in the Supreme Court by the State of Texas: