Here's your 10-point cheat sheet to this big story:
Japan's Prime Minister Shinzo Abe opened the G20 Summit this morning, which will be dominated by contentious discussions on trade, geopolitical tensions, and climate change. But the mood appeared friendly in the opening minutes, with smiles on the faces of the arriving leaders as they posed for the traditional "family photograph".
"Digitalisation has rapidly changed various aspects of our society and economy," Shinzo Abe said as he opened the session, news agency AFP reported. "I'm happy to see the momentum to globally tackle the digital economy."
But in a sign of the ongoing tensions likely to dominate talks, Mr Trump appeared to make reference to US concerns about the security threat posed by Chinese telecoms firm Huawei. As "we expand digital trade, we must also ensure the resilience and security of our 5G networks", he said.
"...Terrorism not only targets the innocent, it creates an environment that is dangerous. We must all make it a priority to do all we can to curb and end terrorism on a global scale," PM Modi said as he exchanged views with Russian President Vladimir Putin, Chinese President Xi Jinping, Brazilian President Jair Bolsonaro and South African President Cyril Ramaphosa of the BRICS grouping.
The development of the global economy is largely driven by one-sided decisions and disputes felt by the entire system, said PM Modi. "We should still focus on the World Trade Organisation (WTO) reform to achieve balanced development of the global economy and so this growth is open to everyone," PM Modi said.
"On Iran, the primary focus was on how we ensure stability there, as instability affects us in many ways, not just in the matter of energy needs, but also in terms of our large diaspora in Gulf. Eight million Indians are in the Gulf," India's Foreign Secretary Vijay Keshav Gokhale told reporters.
The G20 Summit in Japan where world leaders are gathered is one of the most high-stakes and fractious meetings in years, with a bruising US-China trade war, geopolitical tensions, and climate change on the agenda.
G20 Summit host Japan is hoping to bridge the gaps between European leaders who want strong action and an American administration committed to withdrawing from the Paris climate agreement.
The two-day summit in the city of Osaka is dominated by trade issues, with all eyes on whether US President Donald Trump and Chinese President Xi Jinping can reach a truce in a dispute that has been hugely damaging for the world economy. But world leaders will also be seeking to tamp down tensions between Washington and Iran that have led to fears of a new conflict in the Middle East.
Mr Trump also congratulated PM Modi on his party's big win in the national election. The interaction between PM Modi and Mr Trump is significant in view of the multiple disagreements that have cropped up between India and the US, including trade tariffs and an arms deal with Russia. Mr Gokhale said the S-400 missile deal was not discussed.