By Gordon Corera
BBC News security correspondent
The initial investigation of the Indian authorities will focus on two areas - firstly a forensic examination of the scene of the explosions for any clues on the types of explosives and detonators used.
Establishing exactly who was responsible is an urgent task
The second area will be a search for witnesses who may have seen the bombers, coupled with a broader intelligence effort to establish what information there might be about them.
The authorities have already hinted that they had some idea that an attack was in the offing, but did not have specific details.
That may mean they have a strong idea about the identity of the cell.
There are three broad groups of suspects. In the past, the authorities have been quick to point the finger at militant groups such as Lashkar-e Toiba (LeT) and Jaish-e-Mohammad (JeM), whose main cause has been Kashmiri separatism.
Delhi wants to gather hard evidence as to who is responsible
India says such groups have in the past been trained and supported by Pakistan.
Following an attack on the Indian parliament in December 2001, India and Pakistan nearly went to war over claims that Pakistan was supporting or not stopping the activities of these groups.
They are again likely to be high on the list of suspects, although a spokesman for LeT denied responsibility.
The group's spokesman in Pakistani-administered Kashmir said that LeT could "feel the pain of the victims" of the attacks as the people of Kashmir have been suffering "the same pain for the last 17 years at the hands of the Indian security forces".
The spokesman said that an "independent investigation should be carried out... so that the people behind the attack can be exposed".
India has so far been more cautious of pointing the finger of blame towards Pakistan. Delhi wants to gather harder evidence at a time when relations with Pakistan are on a slightly stronger footing.
It was also noticeable that the Pakistani president and prime minister were among the first to condemn the attacks.
The sophisticated nature of the bombings - and their similarity to train bombs in London and Madrid - has led to some speculation of an al-Qaeda link.
While it is true that recent statements from al-Qaeda's number two, Ayman Al-Zawahiri, have mentioned India and Hindus more prominently than in the past, there is as yet no hard evidence of a link to the Mumbai bombings.
A third possibility is some kind of association to the Indian and Mumbai underworld. A set of deadly 1993 bombings in the city - which killed about 250 people - were thought to have been planned by a Mafia don, Dawood Ibrahim.
Indians say they now believe he is based in Pakistan, and that he has developed links to both al-Qaeda and LeT.
If these links have developed, it is possible that the attack could involve some form of co-operation between all three groups.
But on the other hand, such is the paucity of evidence so soon after the blasts that it could be an entirely different group altogether.
Establishing exactly who was responsible is an urgent task, particularly because of the fear of more attacks, but it will also be a sensitive task in which public pressure for answers will grow.