Marxists and anarchists have had differences throughout the history of the international labour movement.
For example Marx and Engels criticised Proudhon, one of the founders of anarchism, because he opposed trade unions and was virulently anti-feminist.
They criticised another key anarchist figure, Bakunin, because he believed workers should not take political action such as building parties and standing in elections. In fact Bakunin looked to the long-term unemployed, beggars, petty criminals, etc., rather than workers, as the key revolutionary force.
Some anarchists opposed the Russian revolution, though others joined the Bolsheviks. The early Communist International encouraged revolutionary worker-oriented anarchist groups to join, arguing that their conception of an "active minority" was an underdeveloped (but apt) conception of a revolutionary party.
During the Spanish civil war, the Stalinists subjected both Trotskyists and anarchists to repression and murder. The Trotskyists criticised the Spanish anarchists - the strongest anarchist movement ever in history - because, in the crunch, they supported the bourgeois "Popular Front" government.
Anarchists can be of many different sorts. The core idea of anarchism is that the state can be abolished immediately, while Marxists believe that a workers' state is necessary to develop the social conditions which will allow the withering-away of the state. Many anarchists are also hostile to any permanent, structured organisation and to any involvement in electoral politics, but that varies.
Individualist anarchists or liberal-reformist anarchists are quite distant from Marxism, but anarcho communists or anarcho-syndicalists are often closer. ("Syndicalism" means a strategy which sees socialism coming through trade-union action alone, without any political-party organisation).
