Huge respect
The patriarch's body was on display in an open coffin surrounded by flowers and flickering candles at the Cathdral of Christ the Saviour, near the Kremlin.
Senior clergy from across the Orthodox Christian world - along with representatives of Roman Catholic, Anglican, and other churches - attended the ceremony which lasted more than five hours.
The ceremony was led by a high-profile bishop, Kirill, who has been elected the Church's temporary leader, and paid fulsome tribute to Alexiy.
"He inherited a church that was weakened by decades of repression.... Now he is leaving behind a church that is strong," he said.
Russia's political leaders were prominent among the mourners. Both President Dmitry Medvedev and Prime Minister Vladimir Putin approached the coffin to pay their final respects.
The deep, sonorous chants of the traditional Divine Liturgy rang out through the cathedral before the standing congregration of black-clad mourners and black-hooded Orthodox nuns.
Some 80,000 mourners visited the coffin inside the cathedral
Russian media broadcast the funeral ceremony live and cancelled entertainment programmes at the request of President Medvedev.
Traffic jams were reported across the city centre, where some streets were closed off in connection with the funeral, and the city authorities called on workers to take the metro to work instead.
Moscow police say 80,000 people filed past Alexiy II's open coffin between Saturday evening and Tuesday morning.
The numbers speak of the huge respect and authority which he commanded, the BBC's James Rodgers reports from Moscow.
The Cathedral of Christ the Saviour is a striking symbol of the Russian Church's resurgence under Alexiy II's leadership, our correspondent notes.
It was blown up by the atheist Soviet authorities in the 1930s, then rebuilt in the 1990s after the collapse of Communism.
