Semiconductors, a significant type of material in the information era, are becoming more and more powerful in the field of quantum information. In the last decades, semiconductor quantum computation was investigated thoroughly across the world and developed with a dramatically fast speed. The researches vary from initialization, control and readout of qubits, to the architecture of fault tolerant quantum computing. Here, we first introduce the basic ideas for quantum computing, and then discuss the developments of single-and twoqubit gate control in semiconductor. Till now, the qubit initialization, control and readout can be realized with relatively high fidelity and a programmable two-qubit quantum processor was even demonstrated. However, to further improve the qubit quality and scale it up, there are still some challenges to resolve such as the improvement of readout method, material development and scalable designs. We discuss these issues and introduce the forefronts of progress. Finally, considering the positive trend of the research on semiconductor quantum devices and recent theoretical work on the applications of quantum computation, we anticipate that semiconductor quantum computation may develop fast and will have a huge impact on our lives in the near future.