The civics-textbook description of a poll monitor’s job is straightforward enough: to be a watchdog of the vote, so candidates, political parties and the public can have confidence that elections are both honest and transparent.

But the work has changed in the aftermath of the 2020 presidential race, when Donald J. Trump and his allies used information gathered by Republican monitors as part of their attempts to overturn the election results.

This year, the party and its allies have recruited an expanded group of monitors — volunteers chosen to observe voting firsthand inside polling places. They include many who believe the 2020 election was stolen and have been trained to be aggressive in the search for fraud.

Their activities include documenting disputes and irregularities at polling places. In some cases, volunteers are given lists of voters whose eligibility they could challenge, according to recordings of training sessions and meetings reviewed by The New York Times.

Many of those voters have been selected using computer programs that experts say use fundamentally flawed methodology.

Such challenges could become part of disputes if an election is extremely close — or used as fodder to try to sow doubt in the results, election officials and other experts say.