December 2004 Estonian Social Democratic Labour Party changed the name to Estonian Left Party (EVP).
According to the statutes of party the party congress elects the Party Chairman and Executive board as well as nominates a consultative Central Council representing all regional organizations. Local policies are developed by local organizations, while central bodies formulate national policies.
EVP lost representatives in parliament on the 2003 elections when they got 2,059 votes (0,4%). In 2007 election, it fell further to 0,1% and again got no seats.