Mathematics Challenge for Young Australians is a unique enrichment program that has been produced annually by the Australian Mathematics Trust since 1991. In its present form, it is divided into four levels and caters for talented students from years 3 to 10. In a typical year, it attracts over 15,000 entries. Individual schools arrange a period of up to four weeks in the first half of the academic year for students to work on their prescribed set of the problems and write full solutions. Limited collaboration among students is permitted and encouraged. There is a strong emphasis on articulating clearly the reasoning in solutions with sound and complete presentation. A guide containing marking schemes is provided for teachers to help them assess their students' work. It also includes discussion points and extension questions, which are relevant to each problem and may be used by the teacher for further enrichment activity. This paper discusses the history, aims, and structure of the program. It describes how problems are designed by the Challenge Committee to engage the students and develop their problem-solving skills. A range of past Challenge problems are presented to illustrate their construction, diversity, levels of difficulty, and relevance to educational objectives.