Here are the 10 latest developments:
"The Agreement for Cooperation in Peaceful Uses of Nuclear Energy marks a historic step in our engagement to build a clean energy partnership," said PM Modi.
The agreement will allow Japan to supply nuclear reactors, fuel and technology to India, which will be the first country that has not signed the Non-Proliferation Treaty or NPT to have such a deal with Tokyo.
The two countries had reached a broad agreement last December during Mr Abe's visit to India, but Japan, the only country to have suffered a nuclear attack, saw strong political resistance to the deal, especially after the 2011 disaster at the Fukushima Nuclear Power Plant.
Tokyo had reservations about such an agreement with a nation that hasn't signed the Non-Proliferation Treaty, and had sought assurances from New Delhi that it would not conduct nuclear tests any more.
India has declared a moratorium on nuclear testing since its last explosions in 1998. But with concerns about neighbours China and Pakistan being nuclear armed, it has not signed the Non-Proliferation Treaty, contending that it is discriminatory.
Japan is a major player in the nuclear energy market and this deal will make it easier for US-based companies like Westinghouse and GE to set up atomic plants in India as both have Japanese investments.
India is in advanced negotiations with Westinghouse Electric, owned by Japan's Toshiba, to build six nuclear reactors in the south - a part of New Delhi's plan to ramp up nuclear capacity ten-fold by 2032.
A joint statement by PM Modi and Mr Abe also made a strong reference to Pakistan. "The two Prime Ministers condemned terrorism in strongest terms in all its forms and manifestations in the spirit of 'zero tolerance'... They called upon all countries to implement the UNSC Resolution 1267 and other relevant resolutions designating terrorist entities," it said, referring to India's bid to get Jaish-e-Mohammed chief Masood Azhar designated as global a terrorist under this resolution.
The Prime Minister landed in Tokyo last night and this morning met Japanese Emperor Akihito. He also addressed top Japanese CEOs and invited investments, saying India has a huge and substantial need for finances and his government is pursuing reform policies to make the country the world's "most open" economy.
From Tokyo, PM Modi, accompanied by Shinzo Abe, travelled to Kobe by the famed Shinkansen bullet train, the technology that will be deployed for the Mumbai-Ahmedabad High Speed Railway. He visited the Kawasaki Heavy Industries facility in Kobe, where high speed railway is manufactured. Japan wants to edge out China in new bullet train deals with India. The competition between Asia's biggest economies for high-speed rail contracts has been intense. China beat out Japan for a line in Indonesia last year, and the two are set to face off again over a proposed Singapore-Kuala Lumpur link.