Varieties of criticism
Conservative criticism has nothing much to do with "left-wing" or "right-wing", because left-wing people are often very conservative, in the defined sense, while right-wing people can also be very radical, in the defined sense. The difference between "radical" and "conservative" has more to do with the belief in whether "a change to something genuinely new" is really possible and necessary. Radicals typically believe strongly that such change is highly desirable and necessary, and that it can be achieved. Their criticism is that there is "not enough" change. Conservative critics, by contrast, are very skeptical about any such change, because they feel the change is really "just another form" of something that already exists.
Libertarian socialism
Left communism is the range of communist viewpoints held by the communist left, which criticizes the political ideas of the Bolsheviks at certain periods, from a position that is asserted to be more authentically Marxist and proletarian than the views of Leninism held by the Communist International after its first and during its second congress. Left communists see themselves to the left of Leninists (whom they tend to see as "left of capital", not socialists), anarchists (some of whom they consider internationalist socialists) as well as some other revolutionary socialist tendencies (for example De Leonists, who they tend to see as being internationalist socialists only in limited instances). Although she lived before left communism became a distinct tendency, Rosa Luxemburg has heavily influenced most left communists, both politically and theoretically. Proponents of left communism have included Amadeo Bordiga, Herman Gorter, Anton Pannekoek, Otto Rühle, Karl Korsch, Sylvia Pankhurst and Paul Mattick.