The MSZP evolved from the communist Hungarian Socialist Workers' Party (or MSZMP), which ruled Hungary between 1956 and 1989. By the summer of 1989, the MSZMP was no longer a Marxist-Leninist party, and had been taken over by a faction of radical reformers who favoured jettisoning the Communist system in favour of a market economy. One of its leaders, Rezső Nyers, the architect of the New Economic Mechanism in the 1960s and 1970s, was elected as chairman of a four-man collective presidency that replaced the old MSZMP Politburo. Although General Secretary Károly Grósz, who had succeeded longtime leader János Kádár a year earlier, was elected to this body, Nyers now outranked him–and was thus now the de facto leader of Hungary.
At a party congress on 7 October 1989, the MSZMP dissolved and refounded itself as the MSZP, with Nyers as its first president. A marginal "Communist" faction led by Grósz broke away to form a revived Hungarian Socialist Workers' Party, now known as the Hungarian Workers' Party, the other successor of the MSZMP.
The decision to declare the MSZP a successor of the MSZMP was controversial, and still carries repercussions for both the MSZP and Hungary. Another source of controversy is that some members of the former communist elite maintained political influence in the MSZP. Indeed, many key MSZP politicians were active members or held leadership positions within the MSZMP (like Gyula Horn and László Kovács).
On economic issues, the Socialists have often been greater advocates of liberal, free market policies than the conservative opposition, which has tended to favor more state interventionism in the economy through economic and price regulations, as well as through state ownership of key economic enterprises. The MSZP, in contrast, implemented a strong package of market reforms, austerity and privatization in 1995-96, called the Bokros package, when Hungary faced an economic and financial crisis. According to researchers, the elites of the Hungarian 'left' (MSZP and SZDSZ) have been differentiated from the 'right' by being more supportive of the classical neo-liberal economic policies, while the 'right' (especially extreme right) has advocated more interventionist policies. In contrast, issues like church and state and former communists show alignment along the traditional left-right spectrum. It is also noteworthy that, according to research, the MSZP elite's positions used to be closer to voters of the SZDSZ than to their own.
Besides a more liberal approach to the economy overall, the MSZP differentiated itself from the conservative opposition through its more recent focus on transforming state social policy from a collection of measures that benefit the entire population, such as subsidies available to all citizens, to one based on financial and social need.
Besides Gyula Horn, the MSZP's most internationally recognized politicians were Ferenc Gyurcsány and László Kovács, a former member of the European Commission responsible for taxation.