In this tutorial review aimed at researchers using nanofluidic devices, we summarize the current state of theoretical and experimental approaches to describing concentration polarization (CP) in hybrid microfluidic-nanofluidic systems. We also analyze experimental results for these systems and place them in the context of recent theoretical developments. We then extend the theory to explain the behavior of both positively and negatively charged, low-concentration, analyte species in systems with CP. We conclude by discussing several applications of CP in microfluidics.