Here are the top 10 points in this big story:
Bengal Chief Minister Mamata Banerjee reacted sharply to Prime Minister Narendra Modi's two-day Bangladesh visit, accusing him of trying to influence voters in the state. Ms Banerjee reminded the Prime Minister of an incident before the 2019 Lok Sabha election - a Bangladesh actor who attended a Trinamool rally had his visa revoked - and asked: "Why shouldn't your visa be cancelled?"
The Trinamool and the BJP have traded allegations of sponsoring violence and vote-rigging all day. Soumendu Adhikari, the brother of ex-Trinamool MLA Suvendu Adhikari - whose crossover to the BJP last year triggered a bitter spat with Ms Banerjee - said he had been attacked by Trinamool supporters in Contai. He said his vehicle had been vandalised and driver injured. '
Suvendu Adhikari - who will take on Ms Banerjee in a high-stakes battle for Nandigram in the second phase - earlier demanded the suspension of police officers in that constituency and Haldi for helping the ruling party in rigging votes.
Trinamool leader Soham Chakraborty, the Chandipur candidate, flagged EVM issues in Kanthi Uttar. "... votes seem to be going to BJP whenever a vote is cast for Trinamool Congress!" he tweeted. Party colleague Derek O'Brien wrote to the Election Commission claiming discrepancies in voter turnout for Kanthi Uttar and Kanthi Dakshin.
Hours before polling began in Bengal, the East Medinipur district witnessed violence - bombs were hurled and shots fired in Bhagabanpur constituency, according to news agency ANI. Two security personnel were reportedly injured. BJP leader Samir Das, meanwhile, told ANI the Trinamool was responsible for violence in West Medinipur also.
Bengal BJP chief Dilip Ghosh, criticised for his "bermuda shots" swipe at Mamata Banerjee, has said the Trinamool is complaining about EVMs because they know they are losing. "TMC and Mamata Banerjee are under pressure and that is why they are saying such things," he told ANI.
In Assam, meanwhile, Chief Minister Sonowal - the biggest name on the ballot - cast his vote at a polling station in Dibrugarh. "I prayed for peace for all...," he told reporters. Mr Sonowal is defending his Majuli seat - a reserved constituency - from the Congress' Rajib Lochan Pegu - a three-time former MLA from this seat.
Other big names contesting in Assam in the first phase were outgoing Speaker Hitendranath Goswami and Assam Congress chief Ripun Borah. Activist Akhil Gogoi, in jail for his alleged role in the 2019 anti-CAA protests, is contesting from Sibsagar. Also voting is Titabor - the seat held for four successive terms by former Chief Minister and Congress veteran Tarun Gogoi, who died in November.
Of the 30 seats in Bengal, the BJP is contesting 29; one has been given to the All Jharkhand Students Union (AJSU). The Trinamool will also contest 29 and support an independent candidate for the other seat. The Congress will contest only five seats. Its allies - the Left parties - will contest the majority; the CPM will fight 18 and the CPI 4.
In Assam, the BJP is contesting 39 of 47 seats in this phase and ally AGP (Asom Gana Parishad) 10. The two parties will go head-to-head in a "friendly contest" in two seats. The Congress - part of a 'mahajot' (grand alliance) - will contest 43, with one each for the AIDUF of Badruddin Ajmal, the RJD, the AGM and the CPIML.
With input from ANI
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