The charge for the working group on high gradient and laser-structure based acceleration was to assess the current challenges involved in developing an advanced accelerator based on electromagnetic structures, and survey state-of-the-art methods to address those challenges. The topics of more than 50 presentations in the working group covered a very broad range of issues, from ideas, theoretical models and simulations, to design and manufacturing of accelerating structures and, finally, experimental results on obtaining extremely high accelerating gradients in structures from conventional microwave frequency range up to THz and laser frequencies. Workshop discussion topics included advances in the understanding of the physics of breakdown and other phenomena, limiting high gradient performance of accelerating structures. New results presented in this workshop demonstrated significant progress in the fields of conventional vacuum structure-based acceleration, dielectric wakefield acceleration, and laser-structure acceleration.