Fluorescent chemosensors for ions and neutral analytes have been widely applied in many diverse fields such as biology, physiology, pharmacology, and environmental sciences. The field of fluorescent chemosensors has been in existence for about 150 years. In this time, a large range of fluorescent chemosensors have been established for the detection of biologically and/or environmentally important species. Despite the progress made in this field, several problems and challenges still exist. This tutorial review introduces the history and provides a general overview of the development in the research of fluorescent sensors, often referred to as chemosensors. This will be achieved by highlighting some pioneering and representative works from about 40 groups in the world that have made substantial contributions to this field. The basic principles involved in the design of chemosensors for specific analytes, problems and challenges in the field as well as possible future research directions are covered. The application of chemosensors in various established and emerging biotechnologies, is very bright.