The Feb. 5 vote was called when the NDP MPP resigned after five months on the job and the previously long-held Liberal seat is now up for grabs.
The most contentious candidate is Glenn Thibeault, who left his job as an NDP MP to run for the provincial Liberals.
Premier Kathleen Wynne asked Andrew Olivier, the Liberals' Sudbury candidate in last June's general election, not to seek the nomination so Thibeault could run.
Olivier in turn accused the Liberals of offering him a job or appointment in exchange and is now running as an independent in the byelection.
The Liberals have denied that they made Olivier any "specific" offers, saying instead that they were hoping to keep him active in the party.
Polls suggest it's a tight race between Olivier, Thibeault and NDP candidate Suzanne Shawbonquit.
The Progressive Conservatives have asked the Ontario Provincial Police to investigate Olivier's allegations. Elections Ontario is also investigating to determine if the alleged actions contravene the Election Act.
The advance polls in Sudbury will be open from 10 a.m. to 8 p.m. from today until Jan. 30.
In all, there are 10 candidates vying for the seat.