The Center for Relativistic Laser Science (CoReLS) was established in December 2012 to explore novel physical phenomena in the relativistic laser intensity regime. The electron motion enters the relativistic regime at a laser intensity of 1018W/cm2, while protons behave relativistically at 1024W/cm2. To tackle the underlying physics of relativistic laser-matter interactions, the center utilizes a 30-fs petawatt (PW) laser facility developed at Gwangju Institute of Science and Technology (GIST). It is a challenging task to reveal the physics of relativistic and ultra-relativistic laser-matter interactions. We examine the fundamental physical processes in atoms, molecules, plasmas, we explore subatomic entities occurring in an ultra-fast timescale (atto- to zepto-second), and we develop high-energy, ultra-short particle (electron, proton, and ion) beams and radiation (X-ray and γ-ray) sources. Sophisticated methods of controlling the spatio-temporal structure of ultra-intense laser pulses are to be developed to precisely manipulate relativistic laser-matter interactions. Such developments will allow us to achieve our goals by steering the interaction processes (e.g., relativistic harmonic generation at extreme orders, mono-energetic electron acceleration over GeV, energetic proton generation with narrow bandwidths; strong X-ray and γ-ray generation).