The thesis considers non-linear probabilistic models for natural language parsing, and it primarily focuses on the class of models which do not impose strict constraints on the structure of statistical dependencies. The main contribution is the demonstration that such models are appropriate for natural language parsing tasks and provide advantages over the use of standard 'linear' methods. We demonstrate this, first, by showing that though exact inference is intractable for the studied class of models, there exist accurate and tractable approximations. Second, we show that using non-linear representations results in powerful feature induction methods simplifying construction of parsers for new problems and domains, and leading to the state-of-the-art performance. Also, we demonstrate that the latent space induced by the model can be exploited in discriminative rerankers, and that this results in the significant improvement both in the standard parsing settings and in domain adaptation.