This paper introduces the concept of two-dimensional bipolar electrochemistry and discusses its principle of operation. The interesting new result is that electrochemical reactions can be localized at particular locations on the perimeter of a two-dimensional bipolar electrode (2D-BPE), configured at the intersection of two orthogonal microfluidic channels, by controlling the electric field within the contacting electrolyte solution. Experimentally determined maps of the electric field in the vicinity of the 2D-BPEs are in semiquantitative agreement with finite element simulations.