Even his own fighters reportedly do not speak about seeing him face to face.
The ISIS chief also appears to wear a mask to address his commanders, earning the nickname "the invisible sheikh".
The Iraqi interior ministry released this image of Baghdadi in January 2014
But Baghdadi - a nom de guerre, rather than his real name - has good reason to maintain a veil of mystery, says the BBC's Security Correspondent, Frank Gardner.
One of his predecessors, Abu Musab Al-Zarqawi who headed the most violent jihadist group in Iraq until his death, was a high-profile showman whose secret location was eventually tracked down. He was killed in a US bombing raid in 2006.
ISIS militants have previously seized parts of Iraq's Anbar province and more recently Mosul and Tikrit
The leader of al-Qaeda's current incarnation in Iraq may be a shadowy figure, but his organisation ISIS is pulling in thousands of new recruits and has become one of the most cohesive militias in the Middle East, our correspondent adds.
Reports suggest he was a cleric in a mosque in the city around the time of the US-led invasion in 2003.
Some believe he was already a militant jihadist during the rule of Saddam Hussein. Others suggest he was radicalised during the four years he was held at Camp Bucca, a US facility in southern Iraq where many al-Qaeda commanders were detained.
The US government released an image of the ISIS leader and offered a reward of $10m
He emerged as the leader of al-Qaeda in Iraq, one of the groups that later became ISIS, in 2010, and rose to prominence during the attempted merger with al-Nusra Front in Syria.
He has not sworn allegiance to the leader of the al-Qaeda network, Zawahiri, who has urged ISIS to focus on Iraq and leave Syria to al-Nusra.
Baghdadi and his fighters have openly defied the al-Qaeda chief, leading some commentators to believe he now holds higher prestige among many Islamist militants.
"The true heir to Osama bin Laden may be ISIS leader Abu Bakr al-Baghdadi," David Ignatiuswrote in The Washington Post.
Zawahiri still has a lot of power by virtue of his franchises in Pakistan and the Arabian Peninsula and North Africa.
But Baghdadi has a reputation as a highly organised and ruthless battlefield tactician, which analysts say makes his organisation more attractive to young jihadists than that of Zawahiri, an Islamic theologian.
In October 2011, the US officially designated Baghdadi as "terrorist" andoffered a $10m (£5.8m; 7.3m euros) reward for information leading to his capture or death.
It notes Baghdadi's aliases, including Abu Duaa and Dr Ibrahim Awwad Ibrahim Ali al-Badri al-Samarrai.
As well as the uncertainty surrounding his true identity, his whereabouts are also unclear with reports he was in Raqqa in Syria.
So there remain more questions than answers about the leader of one of the world's most dangerous jihadist groups.