This paper intends to discuss the trends and characteristics of ageing population in the world and analyze the distribution of ageing population between the more-developed and the less-developed regions of the world. The first section presents the distribution of ageing population in the world and compare the fertility rate, mortality rate, median age, proportion of the young and the old, life-expectancy, population pyramids between the more-developed and the less-developed regions. The second section explores the trends of ageing population and the change of population structure in Taiwan. The factors of rapid increase in ageing population and the ageing speed are compared between the more-developed regions and Taiwan. The third section discusses the various social, economic, welfare, health care, and nursing care problems caused by the rapid ageing population. The conclusion recommends that professionals, scholars, governmental officers, and community leaders should take action in planning the effective national population policy, social security and pension policy, social welfare and health care policy as well as economic development policy to meet the challenges of "population explosion" in the near future.