In connection with the 50th anniversary of Aarhus University, 11 September, 1978, brigadier R.A. Bagnold, F.R.S., was conferred the honorary degree of Doctor of Science. The present paper is the manuscript of the lecture R.A. Bagnold was giving at the faculty of science. In the lecture R.A. Bagnold expreses his views on several aspects of sediment transport in air and water. Among the most famous works by R.A Bagnold are the monograph The Physics of Blown Sands and Desert Dunes, 1941 (Chapman & Hall, London) and the paper Flow of Cohesionless Grains in Fluids, 1956 (Royal Soc.London, Phil.trans.A.249, 235–297). Many of the thoughts presented in the present paper have their roots in these two works.