Amphan was the fiercest Cyclone to hit West Bengal in the last 100 years.
A large part of the state was without power as electricity poles have been blown away.
Mobile and internet services were also down as the cyclone has damaged hundreds of communication towers.
"Never in my life have I seen a cyclone like this in Bengal," said 95-year-old Ashok Roy, a retired school teacher, visibly shaken by the ferocity of the extremely severe cyclone 'Amphan' that left a trail of destruction in half a dozen districts, including Kolkata.
Buses and taxis crashed against each other, small fishing boats turned turtle and grounded planes shook at the inundated Kolkata airport as winds of up to 190 kmph rampaged through West Bengal, already reeling under the coronavirus outbreak and the lockdown caused by it.
On Thursday morning, 45-year-old Jamal Mondal along with his four daughters and wife was jostling outside a relief camp in South 24 Parganas district's Gosaba for two loaves of bread and a tarpaulin sheet to spend the nights at a cyclone shelter.
The migrant worker had returned home from Bengaluru on Monday. But that relief was short-lived. His one-storey mud house was washed away by 'Amphan' on Wednesday night.
"On Monday, when I reached home, I thought my sufferings were over. But I was wrong. The lockdown took away my job and the cyclone took away everything that was left.
"I do not know what would I do next, where would I stay and how would I feed my family," Mondal told a TV news channel.
Half a dozen districts, including large parts of Kolkata, wore a battered look as lakhs of people were homeless and low-lying areas swamped by the cyclone that slammed the Digha coast of West Bengal at 2.30 pm on Wednesday, triggering heavy rainfall in various parts of the state.
Amphan was the fiercest Cyclone to hit West Bengal in the last 100 years.
A large part of the state was without power as electricity poles have been blown away.
Mobile and internet services were also down as the cyclone has damaged hundreds of communication towers.
According to officials, more than 1,500 mobile towers across the state have been destroyed.
In Kolkata, thousands of trees were uprooted, lamp posts unhinged, power supply snapped, and pieces of shattered glass panes littered all over the streets.
Streets and homes in low-lying areas were swamped with rainwater while portions of several dilapidated buildings came crashing down.
"It is not the city where I have grown up... it seems to be a destroyed one. It seems there was a war yesterday... I cannot believe that this is my Kolkata," said Sudhir Chakraborty, a resident of south Kolkata's Rashbehari area.
Cargo and evacuation flights services resumed at the Kolkata International airport since morning even as a portion of the aircraft hanger was waterlogged. Authorities have been trying hard to pump out the water.
Strong winds with speed up to 125 kmph per hour upturned cars in Kolkata and felled trees and electricity poles blocking important roads and intersections.
At Kolkata's Central Avenue, a small concrete temple situated at the base of a banyan tree was uprooted.
More than 4,000 trees, a few hundred electricity poles, traffic signals and police kiosks have been uprooted, a Kolkata Municipal Corporation official.
"The entire city has been devastated. Around 4,000 trees have uprooted in Kolkata. We are short of staff due to the lockdown. It will take some time to restore normalcy," Kolkata Mayor Firhad Hakim said.
More than 14 lakh people in Kolkata are living without electricity since Wednesday night.
Reports from North and South 24 Parganas, and East Midnapore stated that roofs of numerous thatched houses have been blown away.
Embankments in the Sundarban delta -- a UNESCO world heritage site -- were breached as the surge whipped up by the cyclone inundated several kilometres of the islands.
The ecologically fragile Sunderban region, nestled around the world's largest mangrove forest, is home to the endangered Royal Bengal Tiger.
Four jetties in South 24 Parganas collapsed in the Wednesday night's storm.
According to the agricultural department, paddy crop in Burdwan, West Midnapore and Hooghly has been destroyed.
Senior officials said it was too early to estimate the death toll or damage to property as the hardest-hit areas were still not accessible.
"It will take a day or two to assess the complete situation," an official said.
West Bengal Chief Minister Mamata Banerjee, who has been monitoring the situation at state secretariat Nabanna since Tuesday night, said the impact of Amphan was 'worse than coronavirus'.
"There has been massive destruction in the state due to this cyclone. We would give Rs 2-2.5 lakh compensation to the family members of the deceased. We want the Central government to extend financial help to us to tide over the crisis," she said.
"West Bengal is facing an unprecedented crisis. The state's economy was already reeling under pressure from the coronavirus-induced lockdown, and now the devastation by this cyclone has worsened the matter," Banerjee said.
Teams of National Disaster Response Force and State Disaster Response Force have been working on a war footing and deployed heavy machinery to clear the roads blocked by uprooted trees.
More than five lakh people have been evacuated to safety by the state government.
