Did you mean “influence to the 20th century”? In any case I have listed a number of movement covering both the 19th and the 20th.
There are a number of stereotypes purposely poised to compare and apprehend Enlightenment and Romanticism: the difference between Bach and Beethoven, between Science and Literature, or the opposite polarzation of brain and heart,… they all are true (to a limit). The limit being that, like all stereotypes, they do not tell the entire story. A part from such considerations as: “there are great poets in the XVIII century and great scientists in the XIX”, they miss the point that the two movements are not the opposite, but the consequence of one another.
Enlightenment produced the environment necessary for the development of Romanticism. Without the affirmation of scientific reasoning, that came as a consequence of the Scientific Revolution and of the broadening of the academic movement, the Industrial Revolution would not have been possible. And, without the Industrial Revolution, the social and political upsurge that defined Romanticism would not have coagulated.
Hence Romanticism should not be considered a “reaction” to enlightenment. Kant should not be opposed to Hegel. If the former could criticise “pure reasoning” it is because he had absorbed and integrated in his thinking the lucid and structured method of the latter.
As for the second part of the question, unfortunately formulated in such way that it is open to interpretation, my answer is simply: “all of them”. Nihilism, anarchism, nationalism, socialism, positivism… are all children of the romantic generation and form the plinth of a romantic vision of a world inhabited by humans. Realism, surrealism, communism, fascism, environmentalism, emancipation or sociology are their logical sequel. They assign a place to the individual within that world and would have seen a very different light without such notable precursors.
I hope I have rightly interpreted the question and given you the answer you needed.