Who are they?
Germany's oldest political party, the SPD's origins lie in Germany's 19th Century labour movement. Traditionally their support has come mainly from urban populations, especially in Protestant northern Germany and industrial areas such as the Ruhr.
The SPD's most famous leader, Willy Brandt, built up relations between West Germany and the Soviet bloc during his 1970s chancellorship.
But the party's membership has since dropped to around 513,000, after losing thousands of members who became disillusioned with stringent welfare cuts by SPD Chancellor Gerhard Schröder.
This seemed to signal a drift from the left to the political centre by the SPD, a change compounded by the formation of the left-wing Die Linke in 2007, many of whose supporters were disillusioned former SPD voters, unhappy with Schröder's economic reforms.
Who's their leader?
Since gaining his degree in economics from the University of Kiel in 1974, Merkel's challenger for the Chancellorship, Peer Steinbrück, 66, has served as minister of economy, technology and transport for both Schleswig-Holstein and North Rhine-Westphalia before taking the job of finance minister in the CDU-led grand coalition from 2005 and 2009.
Despite his party affiliations and reputed undiplomatic working style, Steinbrück surprised observers by keeping a close working relationship with Chancellor Merkel during his years as finance minister, even making a joint public appearance with her to reassure Germans at the height of the eurozone crisis.
After the SPD left government in 2009, Steinbrück apparently stepped away from high-level politics, making his election as SPD chancellor candidate in 2012 surprising for many.
What's their strategy?
Steinbrück's campaign shows a move back towards traditional social-democratic policies for the SPD. In particular he has thrown his weight behind the introduction of a national minimum wage. The manifesto also includes plans to replace the CDU's child-benefit scheme - which he denounces as an "ideological project" - with investments in state-run day nurseries.
Issues of unethical working hours, conditions and rates of pay have become more contentious and widespread in German politics in recent years, something the SPD has attempted to take advantage of.
As the country's main opposition party it has tried to paint the last four years of rule by the CDU-FDP coalition as four lost years. But with the German economy doing well, Steinbrück has struggled to lay punches on Merkel's CDU.
The SPD has also tried to take advantage of government defence scandals such as the NSA spying programme and misspending by the ministry of defence. But again these have been ineffective, with German voters either not concerned enough or with Merkel able to shrug off the blame, leading her to being called the “Teflon Chancellor”.
Why do they matter?
If Merkel's preferred coalition partners, the FDP, do not pass the five percent vote mark to get into parliament, another grand coalition between the SPD and CDU is likely.
According to polls, this is the most popular of all the potential coalitions which could be formed after the vote on September 22nd.
The second path the SPD could take to power is by forming their own leftwing coalition with the Green Party, but polls suggest the two parties will not get enough of the vote.
Some observers believe they may also form an alliance with the left party, Die Linke, as well as the Greens in a coalition dubbed “rot-rot-grün” – red-red-green. But the SPD leadership has ruled this out.
The Christian Democratic Party (CDU)