He chaired the Dayton talks which eventually brought an end to the fighting in Bosnia and later he was sent by former US president Bill Clinton to talk again to Mr Milosevic as the threat of war grew in Kosovo.
Slobodan Milosevic's death stirs up a lot of extraordinary memories. This man wrecked the Balkans.
He was a war criminal who caused four wars, over 300,000 deaths, 2.5m homeless. Sometimes monsters make the biggest impacts on history - Hitler and Stalin - and such is the case with this gentleman.
As for negotiating with him, of course, I don't apologise for that. So did Lord Carrington, David Owen, Cy Vance, and dozens and dozens of other negotiators.
They all tried to make deals with him. None of them worked. He broke them all.
You're conscious of the fact that you're sitting across the table from a monster
The one I was privileged to negotiate for President Clinton at Dayton worked. It ended the war. As President Clinton said, as [Yitzhak] Rabin of Israel said: 'You don't make peace with your friends, you make peace with your adversaries.'
Negotiating with the man to stop the war, to save tens of thousands of lives which otherwise would have been lost, to prevent the further destruction of Europe, is something that I feel very good about and I have no regrets at all. However, there never was an agreement on Kosovo with Belgrade.
In March 1999 I made two trips to Belgrade at President Clinton's instructions. I told Milosevic that if he accepted our deal and withdrew all his security forces from Kosovo, we would not bomb him.
He refused to do that and as a result I told him, in the last time I ever saw him, I told him that the bombing would start immediately and it would be sustained and severe and he had no response.
He lost first Slovenia, then Croatia, then Bosnia-Hercegovina, Macedonia, finally Kosovo, his job, after his job his freedom
So I got up, I said: 'Well that's it.' He said: 'Will I ever see you again?' I said: 'That's up to you, Mr President' and I left.
I flew directly to Budapest. When I got to Budapest I called Washington and said it's over and the bombing started within a few hours. That's the last time I saw him.
When negotiating with him there are three factors going on. First of all, you're conscious of the fact that you're sitting across the table from a monster whose role in history will be terrible and who has caused so many deaths.
Secondly, you're trying to find enough ground to create an agreement through pressure.
And third, you're dealing with a man who's quite intelligent and who by all accounts had charmed the pants off a generation of diplomats, European and American, congressmen and businessmen.
For example, Larry Eagleburger, who was our ambassador in Yugoslavia when he rose to power and who later became secretary of state, described him in a cable as a Yugoslav [Mikhail] Gorbachev - full of praise for his business skills. That was all wrong.
He wasn't a Yugoslav Gorbachev. Gorbachev did not use force when the Soviet Union started to fall apart. He let it happen peacefully.
Milosevic used force to try to hold Yugoslavia together. As a result he lost first Slovenia, then Croatia, then Bosnia-Hercegovina, Macedonia, Kosovo, his job, after his job his freedom and he ended his days where he deserved to end them - in jail.
It was extremely easy to know what he wanted and we spent a lot of time analysing it and we all reached the same conclusion - he wanted to hold power one more day, and then another day.
He had been a communist, he then switched to being a nationalist. In fact he was neither, he was an opportunist and an opportunist who sought power and wealth for himself.
He was in the great tradition of people like Mobutu [Sese Seko] of Zaire, [Ferdinand] Marcos of the Philippines. There was no serious ideological content to his beliefs.
I never found any core convictions in Milosevic. I don't even feel he was a deep, serious Serb nationalist.
I knew as soon as he reached The Hague that he'd never see daylight again and I think that justice was served in a weird way because he died in his cell, and that was the right thing to do.