This paper reviews recent achievements in sustainability science and discusses the research core and framework of sustainability science. We analyze and organize papers published in three selected core journals of sustainability science: Sustainability Science, Proceedings of the National Academy of Sciences of the United States of America, and Sustainability: Science, Practice, & Policy. Papers are organized into three categories: sustainability and its definition, domain-oriented research, and a research framework for sustainability science. First, we provide a short history and define the basic characteristics of sustainability; then we review current efforts in the following research domains: climate, biodiversity, agriculture, fishery, forestry, energy and resources, water, economic development, health, and lifestyle. Finally, we propose a research framework for sustainability science that includes the following components: goal setting, indicator setting, indicator measurement, causal chain analysis, forecasting, backcasting, and problem-solution chain analysis. We emphasize the importance of this last component for improving situations and attaining goals.