We developed a Gamow shell model based on first principles and successfully applied it to the nuclei around driplines. Herein, we review the theoretical and technical developments of this method. Starting from the realistic nuclear forces, the model uses the Berggren basis, which contains bound, resonant, and scattering continuum states. Therefore, the Gamow shell model can handle the coupling to the continuum. In the complex-momentum plane, we used many-body perturbation theory (i.e., so-called Q^-box folded diagrams) to derive the Hamiltonian for the valence space. Subsequently, the shell-model calculations, which included the resonance and continuum effects, were performed. Therefore, such ab initio calculations can describe the weakly bound properties of nuclei near driplines and unbound resonance properties of nuclei beyond driplines. In this study, the symmetry breaking between oxygen isotopes and their mirror nuclei is discussed, and the important continuum effects on the excitation spectra of neutron-rich carbon isotopes are analyzed.