(CNN) The lawsuits are flying in Florida, as Democrats and Republicans fight over which votes should be counted in the state's hotly contested statewide recount and how long counties should be allowed to count those votes.

To date, there are several lawsuits pending about the recount, with the most litigious group being Democratic Sen. Bill Nelson's reelection campaign, which is hoping the effort will give them a chance at flipping the lead held by Florida Gov. Rick Scott.

Democrats, through the lawsuits, are looking to expand the universe of available votes, primarily by overturning a Florida statute that requires voter signatures on file to match the signatures on mail in ballots, reversing a measure that would allow votes postmarked before Election Day but received after to be counted and by expanding how election officials determine a voters' intent on ballots where a vote is not totally clear.

Nelson's campaign, led by lawyer Marc Elias, and the Democratic Senatorial Campaign Committee are also suing to get rid of the Thursday deadline that requires all counties to finish the machine recount of votes. It appears, due to aging machines, that Palm Beach County will struggle to meet this deadline.

Republicans have also filed their own suits, including one filed by Scott's legal team against controversial Broward County Supervisor of Elections Brenda Snipes and another filed by conservative watchdog Judicial Watch that alleges voter fraud under Snipes. To date, however, there have been no reports of the kind of fraud alleged by Republicans.

Here's a look at the suits in play:

Democrats sue over signature matching

This important hearing happens today at 1 p.m. before Judge Mark Walker in federal court in Tallahassee. Nelson's camp is asking a judge to invalidate Florida rules that say signatures on absentee and provisional ballots must match signatures on file. If successful, that suit could theoretically put thousands of tossed ballots back in play.

Democrats sue to lift all Florida recount deadlines

Nelson's campaign and the Democratic Senatorial Campaign Committee are asking a judge to allow all local elections officials "the time they say is needed" to finish "because the race was so close." There's a status hearing on this Thursday morning before that same judge, Walker, in federal court).

Groups sue to force Rick Scott to recuse himself

The League of Women Voters and Common Cause are asking for a restraining order to stop Scott from exercising any of his powers as governor in relation to the recount. They say he has demonstrated conflict of interest.

Attorneys for Scott told a federal judge Wednesday morning that Scott will recuse himself from the certification of the final election results in Florida.

The comments came during the status hearing in the suit.

While the governor's lawyers said Scott will not sit on the elections board to try to certify the result, that's only a small part of what the plaintiffs are seeking. They want the governor to not have any influence on the election canvassing process or use his authority to suspend election supervisors.

The judge did not make a ruling. A hearing is scheduled for 1 p.m. tomorrow.

Democrats sue over "voter intent" with undervotes and overvotes

Nelson and the Democratic Senatorial Campaign Committee are asking a judge to strike down a state rule that requires voters to use the same method of marking different races in order for such ballots to be counted. For example, the suit argues, the rule would disqualify a ballot where a voter clearly indicated intent by circling a candidate's name in one race but used another kind of marking for different race. Dems believe there are thousands of tossed undervote and overvote ballots in their favor.

During a telephone conference today before Walker, attorneys for both the Nelson campaign and the secretary of state agreed the case is over interpretation of a legal issue and will not require a full hearing before the judge rules.

Walker asked for written filings and responses by tomorrow morning and could rule at any point after that.

Walker noted that there are seven recount-related lawsuits before his court alone, telling the parties: "The people of Florida need to get orders out of me, as well as the parties, sooner rather than later. There's a lot of reasons why time is of the essence."

State house candidate sues to extend recount in Palm Beach County

Democrat James Bonfiglio, in a recount for House District 89, sued to ensure Palm Beach County officials have time to review his race by the deadline. Interestingly, Nelson's team wants a judge to dismiss this case as not to hold up everything else. This case was just transferred from state court to federal court, so the status is unclear.

Democrats sue to allow the count of ballots that arrived late by mail

The VOTEVETS Action Fund, Democratic National Committee and the Democratic Senatorial Campaign Committee are suing the state following the discovery of 266 ballots in the Opa-locka mail facility. The rules say mailed ballots must arrive in elections offices by election night, but the suit argues that voters should not be held responsible for the speed of the US Postal Service. This suit had a status conference Tuesday and Walker set a Thursday deadline for more filings.

Rick Scott is suing the Broward Supervisor of elections

This case in state court asks for an injunction to stop Snipes from counting any ballots not canvassed by last Saturday's noon deadline. This case is pending in Broward's 17th judicial circuit.

Agriculture commissioner candidate is suing the Broward Supervisor of elections

GOP agricuture commissioner candidate Matthew Caldwell, whose race is also undergoing a recount, wants 205 provisional ballots in Broward County declared invalid and no votes received after Election Day counted. This case is pending in Broward's 17th judicial circuit.

Judicial Watch is alleging voter fraud in Broward County

Larry Klayman, the founder of Freedom Watch and Judicial Watch, is suing Snipes, the supervisor of elections for Broward County, for alleged fraud, misconduct and corruption as well as denial of access to the inspection of ballots. This case is pending in Broward's 17th judicial circuit.

Nelson campaign sues Bay County elections official over emailed ballots

Nelson's campaign is suing Bay County's supervisor of elections, who accepted 158 ballots via email or fax from voters who were impacted by Hurricane Michael.

The suit accuses Supervisor of Elections Mark Andersen's office of refusing to allow Nelson's campaign to inspect the ballots and voting records.

"Given the limited period of time for recount results to be certified, Supervisor Andersen's refusal to produce the requested documents not only violates Plaintiff's fundamental right to promptly inspect and copy public records, but threatens the integrity of the voting process by allowing votes to be counted that were not cast by legal means," the complaint reads.

The suit seeks an immediate hearing and a judge's ruling declaring that the documents are public records.

CNN has reached out to the Andersen's office for comment.