First, we will look at some of the praises. At a time when much of the United States was still segregated, Malcolm X spoke out against white oppression using language that few others had dared to do. He preached a message of self-sufficiency as a means of empowerment for young black men, especially those who lived in inner cities. He viewed, initially at least, the approach of Martin Luther King as too gradualist and insufficiently attentive to the social realities of African-Americans. Many, especially in recent years, have praised Malcolm X for calling attention to the systemic poverty that plagued inner-city African-Americans, and the extent to which these economic and social conditions were tied to racism.
As for criticisms, many white liberals at the time perceived Malcolm X as a dangerous radical (a characterization he would not necessarily have rejected.) They thought that King's approach was more constructive, and in fact some historians have noted since that King was highly attentive to social and economic issues, especially late in his life. Others have charged, citing Malcolm X's often incendiary rhetoric, that he promoted violence against whites, and still others have laid the charge of misogyny at his feet. All in all, many have suggested that Malcolm X was a divisive rather than a unifying figure, even within the movement for black freedom itself. It should be noted, however, especially late in his life, that Malcolm X preached an increasingly conciliatory approach, reaching out to sympathetic whites and rejecting the leadership of the Nation of Islam, which he came to view as corrupt and intransigent.
In any case, Malcolm X was a profoundly important leader for young African-American men in the 1960s, and served as a sort of example for the Black Power movement that emerged from the more radical sectors of the civil rights movement. While he has been somewhat overshadowed by Martin Luther King, Jr. in the popular memory, his role should not be underestimated.