Here are 10 big developments on this story:
AAP is leading in 42 seats now, the BJP ahead in only 11, trailing in at least 14 seats it had won the last time. The Congress is leading in three seats.
At the present pace, NDTV's experts project the AAP to win 46 to 50 of Delhi's 70 seats and comfortably form government.
"Delhi voters have voted for AAP... I am confident of an AAP government in Delhi," said AAP second-in-command Manish Sisodia.
Reacting to leads showing AAP ahead, the BJP's presumptive chief minister Kiran Bedi said from her balcony, "The defeat is mine... it is not a referendum on PM Modi."
AAP's Yogendra Yadav had tweeted this morning, "This may be a historic day! The juggernaut likely to halt. David likely to overcome Goliath," referring to Prime Minister Narendra Modi, who addressed a blitz of rallies in the last days of campaigning.
If AAP wins today, it will be the first major setback for PM Modi since he won the national election. The BJP has won most recently held state polls based on BJP chief Amit Shah's strategy of projecting only Mr Modi.
Exactly a year ago, Arvind Kejriwal had quit as chief minister after 49 days in office, over his anti-corruption bill, forcing President's Rule in Delhi.
A giant board at his party office today reads, "Janta ka CM (The chief minister of the people)".
In December 2013, AAP had won 28 seats, the BJP had won 31, the Congress eight. No party was able to get a majority at 36 seats in the 70-member assembly.
A record 67.14 per cent of Delhi's 1.3 crore voters voted in the elections held on Saturday.
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