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During the last several years, the focus of research on resting-state functional magnetic resonance imaging (fMRI) has shifted from the analysis of functional connectivity averaged over the duration of scanning sessions to the analysis of changes of functional connectivity within sessions. Although several studies have reported the presence of dynamic functional connectivity (dFC), statistical assessment of the results is not always carried out in a sound way and, in some studies, is even omitted. In this study, we explain why appropriate statistical tests are needed to detect dFC, we describe how they can be carried out and how to assess the performance of dFC measures, and we illustrate the methodology using spontaneous blood-oxygen level-dependent (BOLD) fMRI recordings of macaque monkeys under general anesthesia and in human subjects under resting-state conditions. We mainly focus on sliding-window correlations since these are most widely used in assessing dFC, but also consider a recently proposed non-linear measure. The simulations and methodology, however, are general and can be applied to any measure. The results are twofold. First, through simulations, we show that in typical resting-state sessions of 10 min, it is almost impossible to detect dFC using sliding-window correlations. This prediction is validated by both the macaque and the human data: in none of the individual recording sessions was evidence for dFC found. Second, detection power can be considerably increased by session- or subject-averaging of the measures. In doing so, we found that most of the functional connections are in fact dynamic. With this study, we hope to raise awareness of the statistical pitfalls in the assessment of dFC and how they can be avoided by using appropriate statistical methods.