Dielectric laser-driven accelerators (DLAs) utilizing large electric fields from solid-state laser system to accelerate particles with high gradients in the range of GV/m, have the potential to realize for the first time an on-chip particle accelerator. Dual-grating structures are one of the candidates for DLAs. They can be mass-produced using available nanofabrication techniques due to their simpler structural geometry compared to other types of DLAs. The detailed geometry optimizations and beam quality studies for dual-grating structures are presented in this talk. Moreover, two kinds of schemes, including adding a Bragg reflector and using pulse-front-tilted (PFT) laser illumination, are proposed to improve the electron energy efficiency for dual-grating DLAs. The detailed analytical calculations and particle-in-cell simulations for both schemes will be presented in this talk. In addition, some progress on the fabrication and experimental studies for dual-grating DLAs are also included in this talk.