WASHINGTON - Germany's Angela Merkel wants to tackle global warming. Britain's Tony Blair seeks help for Africa. President Bush wants to change the subject from Iraq to areas where allied cooperation is possible.
All these hopes for the Group of Eight summit could fall victim to rising tensions with the Russians, who are unhappy over U.S. plans to put an anti-missile system in Moscow's backyard.
Here's a look at the strategies the G-8 leaders will be pursuing at the June 6-8 summit in the Baltic Sea resort of Heiligendamm, Germany.
President Bush is hoping to use his seventh G-8 summit to heal relations frayed by the Iraq war by emphasizing areas where his administration and U.S. allies can agree. He spent the days before the summit rolling out initiatives designed to appeal to foreign critics.
Under international pressure to take action against global warming, the president proposed that the United States and 14 other big polluters spend the next 18 months deciding on a long-term goal for cutting greenhouse gas emissions. While representing a significant change of course for the administration, the Bush plan does not go as far as one supported by Germany and other G-8 nations that would set stringent new emissions limits.
Bush also announced new economic sanctions against Sudan in response to the crisis in Darfur that has killed 200,000 people and called on Congress to double the U.S. funding commitment to help fight the AIDS crisis in Africa and other poor nations.
While Bush is likely to hear less criticism about the Iraq war, he will face a growing rift with Russia over the president's plans to build a missile defense system to guard Europe against attack from nations such as Iran.
Bush goes to the summit with some of the lowest approval ratings of his presidency. A recent AP-Ipsos poll showed that 35 percent of Americans approve of the way he is handling his job, near his all-time low of 32 percent.
President Vladimir Putin, who was last year's host for the G-8 summit in St. Petersburg, is making no secret of his unhappiness over the missile defense plans. In pre-summit interviews, he warned that Moscow could take retaliatory steps if Washington proceeded with a proposal to place a radar system in the Czech Republic and interceptor missiles in neighboring Poland. He suggested the retaliation could take the form of retargeting Russian missiles at Europe.
National Security Adviser Stephen Hadley said Monday the administration wanted to have a "constructive dialogue" with Russia and did not believe the "escalation in the rhetoric" was helpful in that goal.
Putin arrives at the summit with sky-high approval ratings. In a recent poll of Russian voters, 63 percent said they would vote for him again even though he is barred by the Russian constitution from another term. No other Russian politician received more than 4 percent.
Putin's popularity has been aided by an economic rebound fueled by soaring global oil prices. Russia is the world's second largest energy producer after Saudi Arabia.
Putin responded to reporters' questions about the Kremlin's crackdown on domestic critics by detailing what he said were widespread human-rights abuses in other G-8 countries.
Chancellor Merkel has put global warming high on the agenda for this year. She offered muted praise for Bush's new plan, calling it "common ground on which to act." Her proposal, backed by other G-8 nations, goes much further. It calls for limiting the worldwide temperature rise this century to 3.6 degrees Fahrenheit and cutting global greenhouse emissions to 50 percent of 1990 levels by 2050.
Merkel has moved to improve relations with the United States that were severely strained by the anti-Iraq war stance of her predecessor, Gerhard Schroeder. But she has stuck to Germany's refusal to send troops to Iraq.
She is riding a crest of voter popularity, helped by a rebound in the German economy, Europe's largest, after a long period of stagnation. Her popularity has not transferred to her conservative Christian Democrats, who are in a left-right "grand coalition" government with Schroeder's Social Democrats.
Following past practices, Merkel has invited key developing countries - China, India, Brazil, Mexico and South Africa - to attend a portion of the meetings.
Prime Minister Blair, who will leave office after a decade in power June 27, is hoping to use his final G-8 to bolster one of his signature international achievement's: gaining pledges from wealthy nations to double support for Africa.
Derided by critics as "Bush's poodle," Blair's image wasn't helped at last year's summit when an open microphone picked up Bush's greeting of "Yo, Blair," in an exchange seen as underscoring the British leader's junior-partner status in the relationship.
While the G-8 countries have lagged in meeting the goal they set at the summit in Gleneagles, Scotland, to double aid to Africa, Blair's aides expressed hope that the pace of pledges will quicken.
Blair is expected to support any G-8 moves to toughen sanctions against Sudan.
President Nicolas Sarkozy will be attending his first G-8 summit, after having won election to succeed Jacques Chirac. He pledged to pull the sluggish French economy out of the doldrums, in part by engendering a work ethic and making the country more globalization-friendly.
Sarkozy has called the Iraq war a "historic error" but has moved to improve relations with the Bush administration.
On climate change, Sarkozy, after his election, said in a phone call with Bush that the United States has the duty to take the lead on the issue.
Sarkozy is expected to push for deeper cooperation with Africa in part to curb the flow of illegal immigrants into France. He has promised to be a tough bargainer in global trade talks, saying Europe should open its markets only to those who open theirs.
Prime Minister Shinzo Abe, also a newcomer at this year's summit, goes into the meeting politically wounded by money scandals that culminated May 28 with the suicide of his agriculture minister. Support for Abe has plummeted to its lowest level since he succeeded highly popular Junichiro Koizumi last fall.
His troubles are coming less than two months before crucial elections in July for the upper house of parliament. Embarrassing losses in those elections could prompt Abe's ruling party to seek his ouster as prime minister.
Abe has made climate change a summit priority. Japan will also push for a conclusion to the Doha Round of global trade talks and greater efforts to deal with the nuclear programs of Iran and North Korea.
Premier Romano Prodi, leading a center-left government, marked his first year in office in May. Opinion polls have shown a decline in his approval ratings, mainly due to bickering inside his coalition and tough economic measures he has put in place to revive Italy's economy.
Adding to Prodi's troubles, center-left candidates fared poorly in two rounds of local elections. Conservative opposition leader Silvio Berlusconi, the former premier, said the local vote represented "a clear sign of no-confidence" in the government. Opinion polls have shown if an election was held now, Berlusconi's conservatives would win.
Relations between the United States and Italy have been strained since Prodi - whose coalition government includes Communists and other radical leftists - took over from Berlusconi, a staunch Bush supporter. Prodi made good on an election promise and in December completed the pullout of the Italian troops Berlusconi sent to Iraq.
Prime Minister Stephen Harper, who ended nearly 13 years of Liberal Party rule in January 2006, has not fared well during his initial time in office. Polls show his approval rating at 33 percent, down seven points in two months. His government is facing allegations of alleged torture of Afghan detainees handed over by Canadians to Afghan authorities.
Harper initially insisted there was no evidence of torture only to have his government embarrassed when reports emerged that the government had received and then attempted to hide warnings torture was rampant in Afghan prisons. To deal with the issue, Canada reached an agreement with the Afghan government that will allow monitoring of the treatment of prisoners that Canadian soldiers hand over.