During the last decades, researchers discovered and investigated a multitude of cross-dimensional S-R compatibility effects between different stimulus and response dimensions, including quantities, valence, and space. A prominent example is the SNARC (spatial-numerical association of response codes) effect, which describes the fact that human participants are faster and more accurate when responding to small numbers with a left rather than right response, and vice versa. Similar compatibility effects occur when physical size (spatial-size association of response code, SSARC) or valence varies as a stimulus feature, and participants respond with spatially distinct responses. Both the etiology and the structural sources of these compatibility effects are a matter of considerable debate. For many cross-dimensional compatibility effects, both local accounts (e.g., the mental number line as an explanation for the SNARC effect) and global accounts, which attempt to explain several phenomena through a general principle (e.g., a theory of magnitude; polarity correspondence) have been proposed. In this symposium, we present new research on different, cross-dimensional compatibility effects. Two contributions deal with the SNARC effect (Miklashevsky, Lindemann, & Fischer; Wühr & Richter), two talks report on the SSARC effect (e.g., Seegelke & Wühr; Wühr, Richter, & Seegelke), and a fifth contribution is concerned with valence-space interactions (Kühne, Nenaschew, & Miklashevsky). Based on these and other results, we evaluate similarities and differences between different compatibility effects, and discuss the plausibility of global accounts for these effects.