Israeli Prime Minister Benjamin Netanyahu described him as "a great man of the world", as he led the eulogies.
US President Barack Obama said the presence of Palestinian leader Mahmoud Abbas at the funeral was a reminder of the "unfinished business of peace". Mr Abbas was among dozens of foreign dignitaries attending in Jerusalem. Continue...
Security was intensified ahead of the ceremony, with several people arrested.
Delivering an emotional address, Mr Netanyahu said that while Israel and the world grieved for Mr Peres there was hope in his legacy.
"Shimon lived a life of purpose," he told thousands gathered at Jerusalem's Mount Herzl cemetery.
"He soared to incredible heights. He swept so many with his vision and his hope. He was a great man of Israel.
"He was a great man of the world."
Former US President Bill Clinton, who helped negotiate the Oslo peace accords between Israel and the Palestinians in the 1990s, said he was Israel's "biggest dreamer".
"He imagined all the things the rest of us could do. He started life as Israel's brightest student, became its best teacher and ended up its biggest dreamer.''
US President Barack Obama closed the eulogies, comparing Mr Peres to "some of the other giants of the 20th Century that I've had the honour to meet, like Nelson Mandela and Her Majesty Queen Elizabeth".