It remains unclear who carried out the audacious attacks
By Andrew Whitehead
Former BBC India correspondent
Over the past 20 years, Mumbai has suffered vicious communal riots, repeated bomb attacks, persistent gang violence, and political assassinations.
It is India's most prosperous city, its most outward-looking - and also its most volatile.
Still, the scale and sophistication of these audacious attacks will be shocking for the 20 million people who live in and around Mumbai - and for a country whose growing prosperity is in large part built on the city's commercial success.
The targets included the main rail station, one of the world's busiest, and the sort of hotels and restaurants patronised by local and visiting business leaders.
The country has been captivated and horrified by live television pictures of flames leaping from the roof of one of its grandest hotels - and of troops surrounding another Mumbai luxury hotel to root out remaining assailants.
Mumbai has been the target of attacks before, such as in 2006.
For the authorities, the immediate priority is to respond to the emergency and to free those still trapped or held hostage, rather than to attribute responsibility.
India's TV news channels have, in the initial hours of the drama, largely refrained from pointing the finger of blame.
The claim from a little-heard-of organisation, Deccan Mujahideen, may harden suspicions that Islamic radicals are involved.
Two years ago the authorities blamed a series of bomb attacks on Mumbai commuter trains on Islamic militant groups once based in Pakistan.
Back in 1993, a string of co-ordinated attacks on landmarks across Mumbai, bombings which left hundreds dead, were widely believed to have been the work of organised crime.
The Indian authorities held neighbouring Pakistan responsible for organising those bombings, an allegation angrily rejected in Islamabad.
But there are other possible culprits.
Some recent bomb attacks - though on nothing like this scale - have been blamed on militant Hindu organisations.
The motive is far from clear. The choice of targets might suggest an attempt to undermine business confidence and put off foreign investors.
Some may wonder whether the attacks are intended to frustrate attempts to improve relations between India and Pakistan.
Or perhaps they are designed to destabilise the world's largest democracy.
A nationwide election is expected in the next few months, and there are regional elections currently being held in several Indian states.
One is in Indian-administered Kashmir, the Himalayan region whose disputed status has been the main cause of 60 years of tension and conflict between South Asia's two nuclear neighbours.