Peter Taylor: Invited Plenary Lectures Birth of the Tournament of Towns, with NN Konstantinov and JB Tabov, First Congress of World Federation of National Mathematics Competitions, Waterloo, Canada, July 1990. The Growing Competition and Enrichment Scene in Australia, Biennial Conference of the New Zealand Association of Mathematics Teachers, Wellington, New Zealand, September 1991. Howard Lyons Speaker, Canadian Mathematics Competition Seminar, University of Waterloo, Canada, June 1993. Mathematics Assessment in Australia, International Symposium on Assessment in Mathematics and Science, Taipei, Taiwan, April 1998. Mathematics Enrichment Beyond 2000, The Australian Experience and the Role of the WFNMC, Third Congress of World Federation of National Mathematics Competitions, Zhong Shan, China, July 1998. Informatics: The Role of Mathematics, First International Virtual conference on Mathematics Education, Technology and the Classroom, Australian Association of Mathematics Teachers, October and November 1998. Competitions and other methods for motivating talented mathematics students, Conference "Creativity and education of mathematically talented students", Korea Society of Mathematical Education, Kangwon, Korea, October 1999. Mathematics Competitions and their Role in Mathematics Education, Mathe ist TOP, a Conference of Deutsche Mathematiker-Vereinigung in conjunction with the International Year of Mathematics, Gerhard Merkator Universität, Duisburg, September 2000. Competitions, direct and indirect influences on mathematics learning, Conference "Why Mathematics Matters" in conjunction with the International Year of Mathematics, Australian National University, Canberra, 24 November, 2000. Mathematics Competitions and Related Activities and their Role in Mathematics Education, Colloque international de la Commission inter-IREM Rallye, "Rallye Mathématiques, Jeux, Compétitions, Clubs, ...", Université Paul Sabatier, Toulouse, 15 June 2001. The Role of Mathematics Competitions and Related Activities in Mathematical Education, International Conference on Primary and Secondary Schools Science and Mathematics Education, Kuala Lumpur, 22 October 2001. Competitions and Related Activities: Their Role in the Learning Process, Second Internationl Conference "Creativity in Mathematics Education and the Education of Gifted Students", University of Latvia, Riga, Latvia, July 2002. Competitions and Education, Second Pan African Mathematical Union Special Conference on Competitions, Dakar, Senegal, 16 December 2002. Howard Lyons Speaker, Canadian Mathematics Competition Seminar, University of Waterloo, Canada, June 2003. ICMI Study 16: Challenging Mathematics in and Beyond the Classroom, Third Internationl Conference "Creativity in Mathematics Education and the Education of Gifted Students", University of Rousse, Rousse, Bulgaria, August 2003. The Australian Mathematical Sciences Institute and the Making of Mathematicians, Anniversary Lecture, with Garth Gaudry and Jan Thomas, at the Conference of the Mathematical Association of Victoria, Melbourne, 5 December 2003. The Role of Challenge in Mathematics Education, Iranian Conference on Computers in Schools, Isfahan, 02 September 2004. Challenging mathematics and its role in the learning process, Hanna Neumann Memorial Lecture, Australian Association of Mathematics Teachers Biennial Conference, Sydney, 18 January 2005. (lecture also given as Plenary at Iranian Mathematical Society Annual meeting, Ahwaz, 25 January 2005, at Sultan Qaboos University, Muscat, Oman 02 February 2005 as seminar and as Plenary at Colombian Mathematical Society Annual Meeting, Bogota, 09 August 2005). Howard Lyons Speaker, Canadian Mathematics Competition Seminar, University of Waterloo, Canada, June 2007. Mathematical Categorisation of Connecting Tasks, International Workshop of the Israel Science Foundation, Haifa, Israel, 20 February 2008. ICMI Study 16: Current Perspectives, The 5th International Conference on Creativity in Mathematics and the Education of Gifted Students, Haifa, Israel, 27 February, 2008. Also presented in slightly amended form at ICME-11, Monterrey, Mexico, 2008, on 08 July at meeting of WFNMC and on 11 July in plenary session of ICME-11. An Introduction to Probability, Chris Heyde Memorial Workshop, University of Canberra, 29 August, 2008. Asian Success in Mathematics: An Australian Perspective, Conference: Paradigms in Mathematical Education for the XXIst Century, sponsored by Spanish Government and European Union, Valencia, Spain, 22 to 24 October 2009. ICMI Study 16 - The Aftermath, Conference: World Federation of National Mathematics Competitions 6, Riga, July 2010. This lecture, slightly adapted, was also part of an invited lecture for the Mathematics Trainers Guild of the Philippines, celebrating their 15th anniversary, at Tagaytay, October 2010, attended by 520 teachers, from Philippines and nearby countries.