Here's your 10-point cheat sheet to this big story:
PM Modi, 68, and BJP president Amit Shah began the first day of a new term with visits to party patriarchs LK Advani and Murli Manohar Joshi, believed to be upset since they were asked to sit out this election.
"The BJP's successes today are possible because greats like him (LK Advani) spent decades building the party and providing a fresh ideological narrative to the people," PM Modi. The BJP and its allies in the National Democratic Alliance (NDA) are set to win around 350 seats, compared to 336 in 2014, but the BJP's tally will settle at an all-time high.
Addressing party workers who showered rose petals on him and Amit Shah last evening, PM Modi said: "Whatever happened in these elections is in the past, we have to look ahead. We have to take everyone forward, including our opponents."
BJP chief Amit Shah, the architect of the victory, tweeted: "This victory is India's victory. This is the victory of the hopes of youths, the poor, and farmers. This massive win is the victory of Prime Minister Narendra Modi's development and the people's trust in him. On the behalf of crores of BJP workers, I congratulate Narendra Modi."
Congratulating Prime Minister Narendra Modi for the re-election, Congress chief Rahul Gandhi asked him to "take care of the interests of the country". He also conceded defeat in Amethi, asking BJP leader Smriti Irani to nurture the constituency "with love". Mr Gandhi has reportedly offered to resign as President of the Congress, though the party is unlikely to accept.
"The cabinet and Union Council of Ministers will meet this evening. The dates for the swearing-in ceremony and Prime Minister Narendra Modi's visits to various parts of the country are yet to be decided," government spokesperson Sitanshu Kar tweeted.
The Congress's dismal performance was accentuated by party chief Rahul Gandhi losing his stronghold Amethi to BJP's Smriti Irani. Mr Gandhi won from his other seat in Wayanad in Kerala, where the BJP drew a blank. "A new morning for Amethi, a new pledge. You placed your trust in development, grateful to Amethi," Smriti Irani tweeted this morning.
The BJP swept Karnataka, Rajasthan and Madhya Pradesh, the states that the Congress won in the assembly elections last December. The Congress-Janata Dal Secular alliance has been ridden with internal fights and strain for months. It accused the BJP of constantly trying to destabilise it by trying to engineer defections.
The alliance of Mayawati and Akhilesh Yadav could not stop the BJP's onslaught in Uttar Pradesh, the state that sends the highest number of lawmakers to parliament. The BJP and its alliance partner Apna Dal won 64 of the state's 80 seats. The results were a shocker for the opposition, which was expecting the alliance to be as effective against the BJP this time as it was during last year's by-elections in Gorakhpur, Phulpur and Kairana.
The BJP won 17 out of 42 states in West Bengal in a massive improvement over its 2014 performance when it won only two seats. Chief Minister Mamata Banerjee fought hard to preserve her territory as the BJP campaigned aggressively in all the 42 seats. Her Trinamool Congress won 23 seats. "Congratulations to the winners. But all losers are not losers," Mamata Banerjee tweeted.