Traditionally, bonfires are lit in many loyalist areas to mark the start of the annual commemoration of William of Orange's victory over King James II at the Battle of the Boyne in 1690.
The Northern Ireland Fire and Rescue Service said they had resolved 13 bonfire incidents on Tuesday night.
However, it said it was also responding to a "significant number" of other bonfire-related callouts.
The PSNI say they are investigating complaints about "distasteful" materials placed on some bonfires.
Sinn FÃ©in National Chairperson Declan Kearney called on unionist politicians to condemn "hatemongers" who put a replica coffin bearing the image of Martin McGuinness, who died in March, on a bonfire in east Belfast.
"I am directly challenging the leaders of all unionists parties to immediately disassociate themselves and their parties from this and other examples of sectarian hate crime," he said.
Martin McGuinness' son Emmett tweeted: "I am very thankful that I was raised by parent's never to hate anyone or anything. Michelle O'Neill is right, the annual display of hate must end."
Images also emerged on social media of a bonfire in east Belfast draped with a banner carrying a racist message directed at Celtic footballer Scott Sinclair.
In a statement, the PSNI said: "Police are investigating complaints about various materials, some of which are clearly distasteful, placed on the bonfire.
"Where police are aware of a crime being committed, an investigation will follow.
"We take hate crime very seriously and actively investigate all incidents reported to us," it added.
Earlier on Tuesday, a number of homes close to a large bonfire in east Belfast were boarded up to protect the properties from heat damage when the fire is lit.

The plans for the development on the Hatchfield Farm estate in Newmarket, Suffolk, had been approved by Forest Heath District Council.
But last year Local Government Secretary Sajiv Javid refused to accept the decision.
Planning judge Mr Justice Gilbart ruled that Mr Javid's decision was fatally inconsistent and "plainly deficient".
The case will now have to be reconsidered.
Mr Justice Gilbart, sitting in London, quashed the refusal, saying: "The secretary of state has performed a complete and unexplained volte-face in his assessment of the highways impacts of two proposals for development on the same site in Newmarket and has also failed to apply his own National Planning Policy Framework."
The judge said: "There is on any view a requirement for more land for housing and other economic development in the Forest Heath District."
Edward Stanley, the 19th Earl of Derby, brought the legal challenge with Moulton Parish Council and the Rural Parishes Alliance.
The judge said local parish councils had for some time argued that growth in the area should not be dispersed among the rural parishes but concentrated in Newmarket.
Newmarket Horsemen's Group and some others were concerned that development in the town "may have an adverse effect on the horseracing industry that is based there" and lead to increased traffic.
A spokesman for Lord Derby said: "The secretary of state now has a second chance to determine the application. He should take full account of the significant benefits the planning application will bring to Newmarket when making a decision."
The Department for Communities and Local Government said: "We have received this judgment and will now consider our response."
Eleventh night bonfires have been taking place across Northern Ireland.
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Lord Derby has won a key High Court stage of his fight to build 400 homes on his land.