Dielectric wakefield (DWA) accelerator concepts are receiving attention on account of their promising performance, mechanical simplicity, and anticipated low cost. Interest in DWA physics directed toward an advanced high-gradient accelerator has been enhanced by a finding that some dielectrics can withstand very high fields (> 1 GV/m) for the short times during the passage of charged bunches along dielectric-lined channels. In a two-channel structure, a drive bunch train propagates in a first channel, and in the second adjacent channel where a high gradient wakefield develops, a witness bunch is accelerated. Compared with single-channel DWA's, a two-beam accelerator delivers a high transformer ratio, and thereby reduces the number of drive beam sections needed to achieve a given final test beam energy. An overview of multi-channel DWA structures will be given, with an emphasis on two-channel structures, presenting their advantages and drawbacks, and potential impact on the field. Studies aimed to examine charging rate and charge distribution in a thin walled dielectric wakefield accelerator from a passing charge bunch and the physics of conductivity and discharge phenomena in dielectric materials useful for such accelerator applications are presented in a separate paper in the EAAC-2015 conference proceedings.