Noninvasive brain stimulation techniques are used in experimental and clinical fields for their potential effects on brain network dynamics and behavior. Transcranial electrical stimulation (TES), including transcranial direct current stimulation (tDCS) and transcranial alternating current stimulation (tACS), has gained popularity because of its convenience and potential as a chronic therapy. However, a mechanistic understanding of TES has lagged behind its widespread adoption. Here, we review data and modelling on the immediate neurophysiological effects of TES in vitro as well as in vivo in both humans and other animals. While it remains unclear how typical TES protocols affect neural activity, we propose that validated models of current flow should inform study design and artifacts should be carefully excluded during signal recording and analysis. Potential indirect effects of TES (e.g., peripheral stimulation) should be investigated in more detail and further explored in experimental designs. We also consider how novel technologies may stimulate the next generation of TES experiments and devices, thus enhancing validity, specificity, and reproducibility.