Video report by ITV News Correspondent Martin Geissler
Thousands of people have gathered to pay tribute to Martin McGuinness at a candlelit vigil in the republican heartland of west Belfast.
The event off happened hours after crowds in Londonderry accompanied the Sinn Fein veteran's coffin on his final journey home to his Bogside neighbourhood.
The former Deputy First Minister of Northern Ireland's death at the age of 66 was announced on Tuesday morning.
Mr McGuinness, a former IRA chief-of-staff, died in Derry’s Altnagelvin hospital after a short illness, surrounded by his family.
He resigned as Deputy First Minster in January in protest at the DUP's handling of the 'cash for ash' energy scandal, triggering a snap election.
In a statement released on Tuesday morning, his Sinn Fein party said: "It is with deep regret and sadness that we have learnt of the death of our friend and comrade Martin McGuinness who passed away in Derry during the night.
"He will be sorely missed by all who knew him."
Theresa May said Martin McGuinness made an "essential and historic contribution" to Northern Ireland's peace process.
The Prime Minister said the former IRA commander "played a defining role" in leading the Republican movement away from violence. But Mrs May made clear she did not always "see eye to eye" with the former deputy first minister and could "never condone" his terrorist past.
And the Queen has sent a private message to Mr McGuinness's widow, Buckingham Palace announced.
President of Ireland Michael D Higgins led tributes from the Republic, saying Mr McGuinness's death leaves a gap that will be hard to fill.
"The world of politics and the people across this island will miss the leadership he gave, shown most clearly during the difficult times of the peace process, and his commitment to the values of genuine democracy that he demonstrated in the development of the institutions in Northern Ireland," he said.
Mr Higgins said Mr McGuinness, who was reportedly suffering from a rare heart condition, made an immense contribution to peace and reconciliation in Northern Ireland.
His retirement came amid health concerns, but he, his family and colleagues did not specify the nature of his illness.
Sinn Fein president Gerry Adams paid tribute to his lifelong friend, saying: "Throughout his life Martin showed great determination, dignity and humility and it was no different during his short illness.
"He was a passionate republican who worked tirelessly for peace and reconciliation and for the reunification of his country.
"But above all he loved his family and the people of Derry and he was immensely proud of both.
"On behalf of republicans everywhere we extend our condolences to Bernie, Fiachra, Emmet, Fionnuala and Grainne, grandchildren and the extended McGuinness family.
During his time in office Mr McGuinness forged an unlikely friendship with then Democratic Unionist Party (DUP) leader Ian Paisley and the two earned the nickname the Chuckle Brothers.
Lord Norman Tebbit, whose wife was injured in the IRA's 1984 bombing of Brighton's Grand Hotel, said the world "is now a sweeter and cleaner place" after Mr McGuinness's death.
He said: "He embraced the peace process because he was a coward, as almost all terrorists are. He knew that the IRA was finished, it was defeated... being a coward he decided he would seek peace. He found a mug in the shape of Mr Blair and as a result, the IRA, including Mr McGuinness were given get out of jail free cards and were never prosecuted for their crimes whereas British soldiers and policemen are still being prosecuted for what they did in the way of duty to protect the civilian population of Northern Ireland."
But Jo Berry, founder of Building Bridges for Peace, whose father Sir Anthony Berry died in the same bombing, said Lord Tebbit was "not speaking for all".
She said she values Mr McGuinness as an "inspiring example of peace and reconciliation".
Mr McGuinness's successor as the party's leader at Stormont, Michelle O'Neill, paid tribute.
She tweeted: "My heart is broke this morning. We have lost a legend, a giant of a man. I'm very proud to say he was my friend and mentor x."
Democratic Unionist leader and former Stormont first minister Arlene Foster said she offered "sincere condolences".
She said: "First and foremost, Martin McGuinness was a much loved husband, father and grandfather.
"My thoughts and prayers are with his wife and the family circle at this very painful time of grief and loss."
She added that history would record differing views on Mr McGuinness but he had played a pivotal role in bringing the republican movement toward peace.
Former Prime Minister Tony Blair, who was in Number 10 when the Good Friday Agreement was signed in 1998, said: "Whatever the past, the Martin I knew was a thoughtful, reflective and committed individual. Once he became the peace maker he became it wholeheartedly and with no shortage of determined opposition to those who wanted to carry on the war.
"I will remember him therefore with immense gratitude for the part he played in the peace process and with genuine affection for the man I came to know and admire for his contribution to peace."
Former US president Bill Clinton said: "Hillary and I were saddened to learn of the death of Martin McGuinness, who devoted his life to his beloved Northern Ireland. When he decided to fight for peace, Martin was calm, courageous, and direct. And when he gave his word, that was as good as gold.
"As Sinn Fein’s chief negotiator, his integrity and willingness to engage in principled compromise were invaluable in reaching the Good Friday Agreement.
"In the years that followed, he played an even more important role in ensuring that the peace would last—personally overseeing the arms decommissioning, joining the new government as the first Education Minister, and later serving as Deputy First Minister, and doing it all with a sense of humor and fairness that inspired both his friends and former foes."
Mr Clinton added: "He believed in a shared future, and refused to live in the past, a lesson all of us who remain should learn and live by. May he rest in peace."
Former deputy first minister Martin McGuinness "played an immeasurable role" in the peace process, Jeremy Corbyn has said.
The Labour leader, who has often faced criticism for his links to Irish republicanism, said he was "very sad" to learn of the death.
Mr Corbyn controversially shared a platform with Mr McGuinness at a news conference in the House of Commons in 1995.