Methane hydrate has attracted great attention due to its close relationship with current energy and environmental issues. It is of great significance and application value to carry out fundamental scientific research on the problems related to exploitation of methane hydrate， storage and transportation of natural gas and hydrogen in the form of hydrate. The nucleation process is the key first step of the formation of methane hydrate. It is a microscopic process in which methane and water molecules form clusters and gradually evolve into hydrates. Little is known about how hydrates begin to nucleate and decompose at the molecular level， because of the lack of appropriate experimental probes. This article first summaries the current understanding of the structure and properties of hydrates， then follows the review on the study of nucleation process based on the molecular dynamics simulation. Finally， with the emphasis on ultrafast nonlinear optical spectroscopy， the advances on experimental study of hydrate formation process are discussed， and future research directions are proposed.