In past few years, quantum computation and quantum simulation have been developed rapidly. The research on quantum computation and quantum simulation involving medium scale number of qubits will have a development priority. In this paper, we review recent developments in those directions. The review will include quantum simulation of many-body system, quantum computation, digital quantum simulators and cloud quantum computation platforms, and quantum software. The quantum simulation of many-body system will include the simulation of quantum dynamics, time crystal and many-body localization, quantum statistical physics and quantum chemistry. The review of those results is based on our consideration to the current characteristics of quantum computation and quantum simulation. Specifically, the number of available qubits is on a medium scale from dozens to several hundreds, the fidelity of the quantum logic gate is not high enough for several thousand of operations. In this sense, the present research is at the stage from fundamental explorations to practical applications. With these in mind, we hope that this review can be helpful for the future study in quantum computation and quantum simulation.