The decision to drop Russia from the group was taken by its other members - the United States, Germany, France, Britain, Canada, Japan and Italy - in March, after Moscow seized Crimea and annexed it, a move not recognized internationally.
Since then, the EU and the United States have imposed travel bans and asset freezes on senior Russian and Crimean officials and threatened to apply much harder-hitting economic and trade measures if Moscow is deemed for have further destabilized eastern Ukraine.
While Russia retains substantial forces on Ukraine's eastern border, and pro-Russia militias are operating in many towns, presidential elections took place relatively peacefully across the whole of Ukraine last month, which the West took as a signal of Moscow's readiness not to escalate the crisis.
That sense of increased cooperation has raised questions about whether the European Union, with its critical trade and energy ties with Russia, could soon seek ways of drawing Moscow back into the fold, such as allowing it to rejoin the G-8.
Officials responsible for coordinating this week's summit did not rule that out on Tuesday, but said Moscow had a long way to go to prove its intentions were sound and that it was capable of acting like a "normal democratic country".
"It's a bit early at this stage, but I wouldn't rule out the heads of state discussing how they see the future of the G-7 or the G-8," said one European official.
"It was Russia that distanced itself from the G-8 via its actions in Ukraine. It is up to Russia to behave in line with international law and the values of the G-8. That would be the prerequisite for the G-8 to become the G-8 again."
At the same time, another official added: "We cannot exclude that if there is an aggravation of the situation, the EU or the G-7 will have to consider further measures against Russia."
Russia denies that it is behind the revolt in eastern Ukraine. It also asserts the right to protect Russian-speakers in the region.
Economics and trade
The Wednesday-Thursday summit will begin with a dinner to discuss foreign policy, including Russia and EU assistance to Ukraine, as well as Syria, Afghanistan, Mali, the Central African Republic and North Korea, officials said.
Economic discussions on Thursday morning are expected to be dominated by trade, including ongoing EU-U.S., EU-Canada and EU-Japan free-trade negotiations, cooperation on tax avoidance and efforts to sustain the global economic recovery.
"Supporting growth and jobs remains the key priority for the G-7 members and recovery is taking hold," said a summit briefing paper distributed on Tuesday.
"Leaders are expected to call for continued and sustained growth in order to bring down unemployment, particularly among young people and the long-term unemployed," it said, adding that financial reforms including stronger institutions and putting an end to 'too-big-to-fail' banks would also be addressed.
After economics, leaders will discuss energy and climate policy, including efforts to diversify supplies - code in Europe for shifting away from dependence on Russian oil and gas - and reduce carbon emissions via greater energy efficiency.
The summit's last session, over lunch on Thursday, will cover development assistance, including disease control and vaccination programs in Africa and food security.