The three most senior surviving leaders of Cambodia's Khmer Rouge regime have gone on trial accused of genocide and crimes against humanity.

The offences orchestrated and ordered by the ex-leaders, now in their 80s, were among "the worst horrors inflicted on any nation in modern history", a UN-backed tribunal was told. Nuon Chea, 85, also known as Brother No 2, is among the accused. He was the right-hand man of the Maoist regime's supreme leader, Pol Pot, who died in 1998.

The regime's former head of state Khieu Samphan, 80, and Ieng Sary, 86, who was Foreign Minister and the international face of the organisation, are also on trial. All deny their guilt,but the tribunal was told the men reduced a nation into a slave camp based on a brutality that "defies belief to the present day".

The accusations relate to the communist movement's murderous rule between 1975 and 1979. The process of trying its senior figures has taken years. Cambodia originally asked the UN and the international community to help set up a tribunal into the genocide in the mid-1990s, so the much-anticipated start of the case is a crucial milestone. In recent months, the tribunal has become increasingly mired in controversy amid allegations that Cambodia's government was interfering in the proceedings. The situation became so difficult that an investigating judge quit.

Missing from the session was the fourth accused, Ieng Thirith – the regime's "First Lady" and the only female leader to be charged. She was ruled unfit for trial because she has dementia. Judges have ordered her release, but she remains locked up while an appeal by the prosecution is considered. The trial also highlights the challenge of trying to bring about justice so long after the alleged crimes. Up to two million people are believed to have been killed or died of starvation or disease during the Khmer Rouge's rule.

Today, more than half of Cambodia's population is younger than 25 and many have just a passing idea of what happened more than three decades ago. Yet campaigners say it is important that the trial takes place and that justice – however imperfect – is seen to be done.

Ou Virak, whose father was killed by the Khmer Rouge before he was born, and whose family fled the country, heads the Cambodian Centre for Human Rights. He said: "The Khmer Rouge years have left an indelible mark on the collective consciousness of the Cambodian people. The trial of the leaders is something that I, like so many other victims of the Khmer Rouge, thought would never happen."