Investigation is making progress but prime suspects remain elusive

It is the biggest operation the police and security services have undertaken, yet 20 days after the first London bombings, and six days after the second attack, all the main, surviving terrorist figures involved are apparently still at large. So what is happening with the investigation, and what progress has been made?

The intelligence

The bulk of MI5's 2,500 officers are working on the two inquiries. Among the main tasks are gathering intelligence on the movements and communications of the main suspects and their associates. Phone conversations and e-mails, from home and abroad, are intercepted at GCHQ in Cheltenham and the US National Security Agency in Maryland.

MI5's headquarters in London is the base for the Joint Terrorism Analysis Centre (JTAC), an operation involving all the agencies, including MI6, and 11 government departments.

JTAC has come under fire for reducing the UK threat status only a month or so before the bombings. MI5 has been criticised by some for failing to pick up any "chatter" or intelligence.

The make-up of the two terror cells also reveals the difficulties with dealing with such diverse types of terrorists. Three of the 7 July bombers were British-born, of Pakistani origin, and the fourth was a Jamaica-born Briton. None of the killers had committed serious criminal offences, although one had been investigated by MI5 for association with a terror suspect.

Details of the second cell shows they come from Somalia and Eritrea but have lived legally in the UK for more than 10 years. Links are emerging between the two groups, but it is far from certain that they knew of each other.

Police inquiry

Almost all of the Met's 400-strong anti-terrorist branch is working on the two cases, along with an extra 400 dedicated officers and many of the Met's 800-strong Special Branch.

Thousands of the force's officers are involved in the inquiry, including the majority of the 3,000-odd who are trained to carry a firearm.

Teams of officers are trawling through video tapes - more than 20,000 have been seized so far - looking for images of the bombers and their possible contacts. Thousands of witness statements are being analysed, public tip-offs followed up, and seized documents, such as phone records and bills, examined.

But despite the wealth of material the police have yet to arrest any of the four failed bombers, or identify a possible fifth terrorist who dumped a device in north-west London. They also failed to prevent the second attack on the Tube and a bus, which, in many aspects, was a copy of the first deadly assault.

Perhaps surprisingly, considering the numbers of police on duty, and enhanced public vigilance for rucksack bombers, the four would-be suicide bombers managed to escape and disappear. The police are undoubtedly getting closer by the hour to the terrorists but the fear remains the bombers could strike again before they are caught.

The forensics 'goldmine'

Scientific analysis is crucial. The five unexploded bombs have provided important evidence, including names and details found in the rucksacks, a distinctive plastic pot used to house the explosive and the home-made explosive itself. Examination of the suspected bomb factory in New Southgate, north London, and the flat in Leeds where the first batch of explosives was made, is also expected to provide clues to the identity of the terror network. DNA samples, fingerprints and bomb components are also being gathered.

The problem with forensic science is that it can take a long time to produce results. The explosives specialists are still unsure what material was used in the bombs and are baffled by chemicals used by the 7 July bombers.

The shoot-to-kill issue

The shooting of an innocent Brazilian, Jean Charles de Menezes, 27, who was mistaken for a suicide bomber, has been a double blow for the inquiry.

It is a tragedy for the dead man and his family but it has also been a damaging distraction for investigators. For two days, it has taken the public and media focus from the bombers - tip-offs from the public are usually crucial in a major inquiry.

On Monday, the Met wrested back the initiative by releasing two names.But the damage to public confidence - and the possible reluctance among some to help police - from the killing of an innocent man is still unclear.

What we don't know

The police, intelligence agencies and government are not telling us everything because they do not want to compromise on-going operations or tip off suspects who may flee. There is a growing concern that the obvious intelligence vacuum on such a secretive grouping of individuals is causing problems, and that the authorities are struggling to make a quick breakthrough.

The prospects of a new attack

PUBLIC TRANSPORT

The Tube and bus network in London is still the most likely target, assuming terrorists can get their hands on workable explosives. With two million people using the system in the capital every day, it is incredibly hard to stop a suicide attack. Extra security measures are in place but they failed to prevent a second suicide attempt. An easier target may be a big multi-ethnic city outside London.

A LORRY OR CAR BOMB

The device that police and security services have been dreading for years. Unless terrorists are stopped while assembling a vehicle bomb, it is extremely hard to prevent. Concrete and steel barriers have been erected at high-profile targets such as the Palace of Westminster, and police marksmen have been told to shoot to kill if necessary. But there are numerous " soft" targets, such as shopping centres, tourist attractions, theme parks and nightclubs. Al-Qa'ida has huge experience in making vehicle bomb, but bombers on the run may not have the time and resources needed to assemble a vehicle bomb.

CONVENTIONAL ATTACK

The four men did not expect to live so are unlikely to have a ready source of usable explosives close at hand. In which case, they could use more conventional weapons, such as guns or knives, to carry out random attacks.

CHEMICAL, BIOLOGICAL OR NUCLEAR

Nothing has been recovered to suggest the group has access to any of these methods of attack.

SUICIDE

The disappearance of the terrorists has led to speculation that they have taken their own lives, but there is no evidence yet to support the suicide theory.