This talk aims to explore some aspects of the relationship between two major strands in current linguistics, viz. cognitive linguistics and functional linguistics. The talk consists of two parts: The first part will offer a general overview and a comparison of the most important features and properties of cognitive linguistics and functional linguistics, in an attempt to get to a better understanding of what both strands share and how they differ. The second part will be devoted to a more detailed analysis of one specific but very crucial issue which appears to divide the two strands, more than anything else, viz. the question of the difference between a constructionist approach to grammar, common in cognitive linguistics, and what may be called a processual approach to grammar, common in functional linguistics.