The 10~30 days extended-range weather forecast has attracted great attention from academic communities around the world, and this forecast plays a significant role in the decision-making process of disaster prevention and reduction. The extended-range forecast shall be combined with the initial meteorological conditions and influencing factors of ocean, atmosphere and climate, in which the observation data feature complexity, comprehensiveness and globalization. All of these scientific big data reflect and present complicated natural phenomena and relations, and are characterized by high data dependency and multiple data attributes, as well as extremely complicated forecast processes. Several methods involving extended-range weather forecast are analyzed from the numerical modeling, statistics and big data methods based on the intraseasonal oscillation and other methods, and the advantages and disadvantages of various types of prediction methods are also compared. Next, the scientific problems in the field of extended-range weather forecast are discussed and summarized. Finally, this paper gives a future prospective of the research for the methods of extended-range weather forecast and its applications.