This article presents a summary of theory, experimental studies, and results for the electrokinetic transport in small fluidic nanochannels. The main focus is on the effect of the electric double layer on the EOF, electric current, and electrophoresis of charged analytes. The double layer thickness can be of the same order as the width of the nanochannels, which has an impact on the transport by shaping the fluid velocity profile, local distributions of the electrolytes, and charged analytes. Our theoretical consideration is limited to continuum analysis where the equations of classical hydrodynamics and electrodynamics still apply. We show that small channels may lead to qualitatively new effects like selective ionic transport based on charge number as well as different modes for molecular separation. These new possibilities together with the rapid development of nanofabrication capabilities lead to an extensive experimental effort to utilize nanochannels for a variety of applications, which are also discussed and analyzed in this review.