Abstract: Theoretical and experimental research on ultracold molecules in recent years has made remarkable achievements, and greatly extended the domain of atomic, molecular and optical physics. Various completely new fields such as high resolution molecular spectroscopy,quantum manipulation of molecular states, precision measurement and quantum simulation have been initiated, centered on the production and application of ultracold molecules. Currently,efficient creation of ultracold dense molecules is mainly realized based on the photoassociation of laser pre-cooled ultracold atoms. This article summarizes the status of the preparation of ultracold molecules by photoassociation, and reviews the physical mechanism and experimental production of ultracold molecules using photoassociation, Feshbach resonance, stimulated Raman adiabatic passage (STIRAP), and ultrashort pulse photoassociation. To conclude, some experimental results and potential applications for the manipulation of ultracold molecules via external fields are presented.