In the past years, superconducting quantum computation has received much attention and significant progress of the device design and fabrication has been made, which leads qubit coherence times to be improved greatly. Recently, we have successfully designed, fabricated, and tested the superconducting qubits based on the negative-inductance superconducting quantum interference devices (nSQUIDs), which are expected to have the advantages for the fast quantum information transfer and macroscopic quantum phenomenon study with a two-dimensional potential landscape. Their quantum coherence and basic physical properties have been demonstrated and systematically investigated. On the other hand, a new type of superconducting qubit, called transmon and Xmon qubit, has been developed in the meantime by the international community, whose coherence time has been gradually increased to the present scale of tens of microseconds. These devices are demonstrated to have many advantages in the sample design and fabrication, and multi-qubit coupling and manipulation. We have also studied this type of superconducting qubit. In collaboration with Zhejiang University and the University of Science and Technology of China, we have successfully fabricated various types of the coupled Xmon devices having the qubit numbers ranging from 4 to 10. Quantum entanglement, quantum algorithm of solving coupled linear equations, and quantum simulation of the many-body localization problem in solid-state physics have been demonstrated by using these devices. Also, we have made significant achievements in the studies of the macroscopic quantum phenomena, quantum dissipation, quantum microwave lasing, and some other quantum optics problems. In particular, Autler-Townes splitting under strong microwave drive, electromagnetically induced transparency, stimulated Raman adiabatic passage, microwave mixing, correlated emission lasing, and microwave frequency up-and-down conversion have been successfully studied, both experimentally and theoretically.