The trial is being held before presiding Judge Chile Eboe-Osuji, from Nigeria, with Judges Olga Herrera Carbuccia and Robert Fremr, from the Dominican Republic and Czech Republic, respectively. It is expected to last for several months.
Avoiding a power vacuum
After the disastrous 2007 election, Kenyatta and Ruto teamed up and formed a coalition, which won the most recent poll held this year.
Jittery Western nations watched as the two took office in April, raising the prospect of complicated diplomatic ties.
Kenyatta maintains that they will cooperate with the court to clear their names and has asked that their proceedings be held on different days to avoid a power vacuum.
"We will work with ICC, but it must understand that Kenya has a constitution. Ruto and myself cannot therefore be away at the same time," he said.
The court has encountered a number of obstacles leading up to the trial.
Charges against three other suspects were dropped for lack of evidence after witnesses dropped out or recanted their testimonies.
Bensouda has previously said that some of the witnesses, including a few who were set to testify against both leaders, pulled out because of intimidation.
Lawyers for Kenyatta and Ruto have denied any witness intimidation.
The ICC was set up in 2002 to try claims of genocide, crimes against humanity and war crimes.
Kenya's previous administration reneged on a deal to set up a special tribunal to try suspects in the post-election violence, forcing the international court to step in.
"The ICC is not, under any circumstances, a substitute for domestic criminal justice systems; it only intervenes if the national judicial system is either unwilling or unable to ensure that justice is done," the court said in a statement.
That message was repeated by the prosecutor in her opening statement.
The ICC intervened "only after the Kenyan efforts to establish a domestic mechanism to investigate the violence failed," Bensouda said.
Ahead of the trial, rights group Amnesty International urged Kenyan authorities to cooperate fully with the ICC to ensure a fair and effective process for those directly involved in the case, and for the Kenyan people.
"Six years after post-election violence rocked the country, it is high time to prioritize the pursuit of justice for the hundreds and thousands of people who lost their lives or homes," said Netsanet Belay, Amnesty International's Africa program director.
"The government's recent efforts to politicize the ICC trials are deplorable, and must not be allowed to affect the commencement and future proceedings of this landmark trial.
"The authorities should focus their energy on ensuring justice, truth and reparation for the victims of many other crimes that the ICC is not able to deal with."
Eyes on Kenya
Kenya is the second African nation after Sudan to have a sitting president facing charges at the International Criminal Court.
It is East Africa's biggest economy and a crucial trade route into the rest of the continent, so neighboring nations are watching the trial keenly.
Kenya provides an important buffer of stability in a region that includes the fledgling Somali government and the politically tense Sudan and South Sudan.
Most importantly -- at least to the West -- Kenya is a major U.S. ally in the war against Islamist militants in the region and has remained relatively peaceful amid civil wars in neighboring nations.