Ultrafast controlling of atomic and molecular quantum states has attracted intensive attention benefited from the development of ultrafast laser and its manipulation. The related researches have led to increasing understanding of the interaction between intense laser field and quantum states of atoms or molecules. In the present paper we review the research progress in this field, particularly focusing on the quantum control of molecular rotation and dissociation in ultrafast laser fields, ionization of atoms and molecules in such ultrafast manipulated laser fields, and prospects for future development.