This talk will be divided into three parts. First I will provide some arguments about why we might want to investigate neural oscillations in relation to cognitive phenomena in the first place. I will then present some data investigating embodied semantics in Spanish using mu oscillations as an index of motor-related cortical activity. Finally, I will offer some (very) preliminary findings from a study investigating the relationship between theta and beta oscillations and the processing of agreement relations (and violations) in Dutch.