Hegel occupies a contradictory position in critical theory. On the one hand, his insights are crucial for the success of the project. On the other, most critical theorists love to show his limitations, and the ways in which he represents just what is wrong with philosophy.
Hegel's thought is complex and wide-ranging, and we cannot give an overview here in any kind of comprehensive way. The best that we can do is to identify a common thread that runs through his work.
Hegel makes it possible to see everything in human culture and knowledge as part of a historical continuum. He believes that all of history culminates with him, or with his time, because his is the first time when people realize this and are able to reflect philosophically on all aspects of human experience. Previously, we simply engaged in science, art, religion, or whatever. Now, we can reflect on it, which means to understand how it developed toward a kind of coherence. The ultimate goal of history is the development of "Geist", a German word translated as both "spirit" and "mind".
This movement through history happens based on conflict. Each idea has contained within itself its own opposition, which becomes apparent as time goes on. Conflict grows in society, and is ultimately resolved by a kind of leap to a new concept that synthesizes the previous contradiction.
An example: the idea of freedom. People at previous times used the term, and may have thought of themselves as free. The Greeks, for instance, had the concept of freedom. Hegel points out, though, that their freedom did not apply to everyone. As time went on, this became more apparent. It took the Romans to enshrine freedom into law, so that it applied to everyone. But the contradictions in the Roman system became apparent over time as well, and this ushered in new ideas of freedom that came in the Christian West.
Hegel tells these stories of progress through history in a variety of ways. He tells, for instance, about how we came to true consciousness (or, perhaps, are still coming to it). He tells about how our art progressed through time to the point where it could fully grasp human experience. He tells about the progress in science, and in religion and philosophy. He tells of the progress of the state. It is the same story, in different areas.
Hegel contributes the idea of historicism to critical theory, the idea that nothing is eternal, not even knowledge, truth, or reality, but that it is always linked to historical conditions.
Put simply, Hegel's progressivism. Hegel believes that everything culminates in European civilization; at least, that's the conservative interpretation of his work. He says:
"What is real is rational, and what is rational is real."
Conservative thinkers interpret this to mean that all history has come to an end, and that the conditions that exist are the perfect conditions. Radical thinkers interpret this to mean that the rational can now be understood, but the real still has to catch up.
Through most of the 19th century, the conservatives won out. However, there were famous radical heirs of Hegel, most notably Marx.
Problems with Hegel's thought:
1. It is modernist, in the sense that it tells a grand story that accounts for everything. What if you don't want to ascribe to that story? Can that story deal with a fundamentally different story? No - it must translate it into its own terms.
2. Other cultures are left out. Africans, particularly, fare badly in Hegel's account. Note what he says about Africans:
The Negro, as already observed, exhibits the natural man in his completely wild and untamed state. We must lay aside all thought of reverence and morality -- all that we call feeling -- if we would rightly comprehend him.
They have moreover no knowledge of the immortality of the soul, although spectres are supposed to appear. The undervaluing of humanity among them reaches an incredible degree of intensity. Tyranny is regarded as no wrong, and cannibalism is looked upon as quite customary and proper. Among us instinct deters from it. . . But with the Negro this is not the case, and the devouring of human flesh is altogether consonant with the general principles of the African race; to the sensual Negro, human flesh is but an object of sense -- mere flesh.
Another characteristic fact in reference to the Negroes is slavery. Negroes are enslaved by Europeans and sold to America. Bad as this may be, their lot in their own land is even worse, since there a slavery quite as absolute exists; for it is the essential principle of slavery, that man has not yet attained a consciousness of his freedom, and consequently sinks down to a mere Thing -- an object of no value.
We could quote many more passages, but it is clear from this that Hegel needs a group of people to "start" the dialectical path. His account of Africans is shocking to modern ears, as his dismissal of them is complete. Critical theory finds this unacceptable, and akin to the kinds of attitudes that it found in German fascism.
3. The concept of progress is a controversial one. Some critical theorists hold to it, believing that we still have a way to go. Others reject it, believing that we are not moving toward any kind of grand telos, but rather simply find ways to live in the times we have before us.