Gov. Philip D. Murphy of New Jersey is barred by term limits from running for re-election, and the specter of an open seat has unleashed fierce battles among Democrats and Republicans hoping to succeed him.

Before the general election in November, each party will choose a nominee in a June 10 primary. Mail-in voting began more than a month ago, and early in-person voting starts on Tuesday.

Here’s what you need to know:

Who is running?

Democrats will choose from among six prominent candidates.

They are: Mayor Ras J. Baraka of Newark; Mayor Steven Fulop of Jersey City; Representative Josh Gottheimer, of the state’s Fifth Congressional District; Representative Mikie Sherrill, of the 11th Congressional District; Sean Spiller, the president of the state’s largest teachers’ union, the New Jersey Education Association; and Stephen Sweeney, a former State Senate president.

Mr. Spiller is the only candidate who failed to reach the $580,000 fund-raising threshold necessary to qualify for matching state funds and to participate in debates. He has benefited from an extensive advertising campaign paid for by a super PAC funded by dues contributed by his union’s members.

The Republican race features three prominent candidates: State Senator Jon M. Bramnick; Jack Ciattarelli, a former state assemblyman; and Bill Spadea, a longtime radio host. Mario M. Kranjac, a former mayor of Englewood Cliffs; and Justin Barbera, a contractor, are also running.

Each party held two state-sponsored debates. All were streamed live and can be viewed online.

Early machine voting

To cast a primary ballot, voters must be registered as a Democrat or Republican, or be prepared to declare a party affiliation. Voters can determine if they are already registered to vote by checking the state’s elections website.