Cognitive effects of anxiety have been amply documented. Anxiety has been linked with an attentional bias toward threat, distractibility, and reductions in short-term memory (STM) capacity. These three functions have rarely been investigated jointly and permeability may account for some of the effects documented. In this experiment, we examine these three cognitive functions using one verbal and one visuospatial task. In the irrelevant speech paradigm, participants had to remember strings of letters while irrelevant neutral or threatening speech was presented. In the visuospatial sandwich paradigm, participants were asked to remember sequences of visuospatial targets sometimes presented within irrelevant distracters. We examined the links between state anxiety, worry, and indices of attentional bias toward threat, distractibility from neutral stimuli, and STM capacity. Results show that state anxiety was uniquely linked with impairments in STM while worry was more particularly related to distractibility, independently from permeability between the different cognitive functions. Attentional bias toward threat was linked with variance common to both anxiety and worry. An examination of clinical and non-clinical subgroups suggests that subjective threat perception and attentional bias toward threat are features that are particularly characteristic of clinical levels of anxiety. Our findings confirm the important links between anxiety and basic cognitive functions.