This dissertation describes a study of Raman coherence effects using superconducting quantum circuits. Raman coherence can occur in a three-level system driven by two coherent electromagnetic fields. In a suitable system with a metastable state, the effect is typically manifest as coherent population trapping (CPT) and electromagnetically induced transparency (EIT). I derive the theoretical framework and show experimentally that in the case of a cascade three-level system based on transmon superconducting qubit states, an effect known as the Autler-Townes doublet (ATD), rather than CPT or EIT, occurs. I propose, model, and implement a quasi- system made of combined transmon-cavity levels, which has a meta-stable state required for CPT and EIT. I measure CPT, and demonstrate coherence of the dark state in the time domain. Instead of EIT, I observe a new phenomenon – electromagnetically suppressed transmission (EST). The large negative dispersion accompanying EST leads to superluminal pulse propagation in the system. My results suggest that quantum superconducting circuits provide a viable platform for studying quantum optics of multi-level systems.