Voting posters in Hong Kong
BBC
Hong Kong voters are electing a new legislature, with pro-democracy candidates expected to benefit from weeks of anti-China protests.
The government has had to scrap plans for mandatory Chinese patriotism lessons in schools after public uproar.
For the first time, 40 of the 70 seats on the governing legislative council will be directly elected, reports the BBC.
The results of the poll could keep on track plans for universal suffrage, which could come as early as 2017.
But for the promised reform to be implemented, it needs the support the legislative council.
Polls in Hong Kong - which has a semi-autonomous status in China - opened at 07:30 local time (23:30 GMT on Saturday) and will close at 22:30.
About 3.5m people are eligible to cast their ballots. Results are not expected until Monday.
The election campaign has been dominated by issues such as employment, corruption and the growing number of visitors from mainland China.
Hong Kong, which was handed to China by Britain in 1997, enjoys greater political freedom than mainland China, including a free press and the right to peaceful assembly.
Under the current laws, 30 of the 70 seats in the assembly are being chosen by small group of electors selected along economic and professional lines.
But the pro-democracy candidates running for office are expected to benefit from the growing anger against mainland China and the lack of political reform there, says the BBC's Hong Kong correspondent Juliana Liu.
A strong showing by the pro-democracy forces this time round could make the transition to universal suffrage more likely in the future, she adds.
For the past week, thousands of demonstrators have camped out around Hong Kong's government headquarters, protesting against the plan for mandatory patriotism lessons.
They said the lessons were Communist Party propaganda and whitewashed events such as the 1989 crackdown in Tiananmen Square and the famine under Mao Zedong.
But the government said the goal was to foster a sense of national belonging.
The proposed curriculum, which consisted of general civics education as well as more controversial lessons on appreciating mainland China, was due to be introduced in primary schools in September and secondary schools in 2013.
On Saturday, Hong Kong's chief executive, Leung Chun-ying, said the classes would be optional for schools.
Leung, who was sworn in as Hong Kong's chief executive in July, cancelled his trip to the Apec regional summit this weekend because of the furore.