New York

Much of the attention on Tuesday will be on a Republican race on Staten Island, where Michael Grimm, a former congressman who pleaded guilty to felony tax fraud in 2014, is running to regain his seat in the 11th District.

Mr. Grimm is facing Representative Dan Donovan, the Republican who succeeded him. A victory by Mr. Grimm would give Democrats an opening in solidly Republican territory, as they will aggressively use Mr. Grimm’s criminal record against him.

Democrats plan to compete hard this fall across New York State, where they hope to pick up Republican-held House seats in regions as varied as the suburbs of Long Island and the farmland along the border with Canada. But crucial races Tuesday will also focus attention on intraparty competition involving four incumbents in and around New York City. Though they are favored to win, the incumbents have faced aggressive challenges from insurgent candidates.

The most closely watched race will be in the 14th District, where the 10-term incumbent Joseph Crowley has been challenged by Alexandria Ocasio-Cortez, a progressive candidate who has called for dismantling the Immigration and Customs Enforcement agency.