The men believed to have masterminded the 2004 bombing of the Australian embassy in Jakarta, and built the bombs used in other recent attacks, are still on the run.
Azahari Husin is thought to have run bomb-making courses
Police have been on their trail since the 2002 Bali bombings.
Two men are believed to have built the bombs used in that attack.
Azahari Husin, a 45-year-old Malaysian university lecturer, and Dulmatin, a 32-year-old electronics expert, were named as chief bomb-makers by another suspect, Ali Imron, who was given a life sentence for his role in the attack, and who has co-operated with the police.
Both men are believed to belong to the militant Islamic group Jemaah Islamiah (JI), accused of carrying out the Bali bombings.
JI, which has often been linked to al-Qaeda, is believed to control a network stretching across Indonesia, Malaysia, the Philippines, Singapore and Thailand. Smaller cells might also exist in Cambodia, Vietnam, and even Australia.
Its principal goals are the establishment of Islamic governments across the region, followed by the formation of a unified South East Asian Islamic state.
Azahari Husin is alleged to be JI's top bomb-making expert.
The group is accused of the 2003 Marriott bombing as well
He gained a doctorate from Britain's University of Reading, and used to work as a former university lecturer in Malaysia.
A married father of two, he is said by some to be a fanatic, ready to die for his cause.
He is believed to have given bomb-making classes to JI militants, and to have issued precise instructions on how the massive car bomb used at the Sari club in Bali was to be manufactured.
As well as technical bomb-making expertise, he is also alleged to have been a key figure at the JI planning meeting which selected Bali as a target.
Dulmatin, also known as Joko Pitono and nicknamed Genius, is a technician and electronics expert.
He is believed to have worked with Azahari Husin to assemble the massive car bomb as well as the explosives vest used by a suicide bomber who attacked the nearby Paddy's Bar, just moments before the explosion at the Sari club.
Indonesian police were successful in catching up with most of the group which carried out the bombings, and several are now in jail and facing execution.
But Azahari Husin and Dulmatin have managed to evade the police hunt, sometimes by the narrowest of margins - police think they have come within minutes of catching Azahari Husin on different occasions.
Since the Bali attacks, Azahari Husin has been more closely linked with another Malaysian, Noordin Mohammed Top.
The two are believed to have built the bomb used in the 2003 attack on Jakarta's JW Marriott hotel, and to have masterminded the September attack on the Australian embassy.
Analysts point out that as long as such men remain at large, the threat of further attacks in Indonesia remains very much alive.
The group they are alleged to belong to, JI, was formed in the mid-1980s by two Indonesian clerics. It evolved its terrorist edge in the mid-1990s when one of its founders, the late Abdullah Sungkar, established contact with Osama Bin Laden's al-Qaeda network, academics and intelligence experts believe.
While Abdullah Sungkar oversaw JI's political and strategic development, several South East Asian intelligence agencies name Abu Bakar Ba'asyir as the group's spiritual leader.
He is currently on trial facing charges relating to the 2002 Bali attacks and the 2003 Marriott hotel bombing in Jakarta.