Theoretical linguists are trying to device models of how natural languages work. Language is a complex system involving at least meaning (semantics), form (phonology, syntax) and pragmatics (the way the context affects the interpretation).Linguists try to characterise in an explicit way how these dimensions of language need to be represented in order to give an adequate account of language production and comprehension. As in most natural sciences, there is a huge gap between the empirical foundations (in our case data from individual langauges and speakers) and the theoretical models that linguists build in order to account for the way language works. This gap makes it hard for non-linguists to understand the issues that linguists are discussing, since these issues are cast in terms that are heavily dependent on a particular theoretical model. I plan to introduce linguistic methodology and evaluation procedures, discuss whether it makes sense to look for universal patterns in language (the so-called Universal Grammar) and hopefully arrive at a better understanding of the way linguists model the interaction between different linguistic subsystems.We will look at the models assumed in constraint-based grammar (Head-driven phrase structure grammar HPSG), transformational grammar (the Minimalist Program) and the general approach taken in Optimality theory (OT).