The subject of river sediment transport has been studied from centuries - by river engineers as well as geographers, geologists, river morphologists and fluvial geomorphologists. Up to now there are no well known complex methods and/or approaches with help of which one can determine the intensity of sediment transport. However, even the approximate knowledge of the quantity of sediment transport is important, especially when dealing with sedimentation of river deltas, and lakes, designing artificial water reservoirs and planning any river engineering works or designing hydraulic structures. The appropriate assessment of the intensity of sediment transport has the direct influence on an adequate functioning of any hydraulics structure or object, with the help of which the negative influence of sediment transport is eliminated (erosion, channel cutting, filling-up river and water reservoir water intakes). One has to bear in mind that all phenomena connected with sediment transport are very complicated and complex and belong to the most poorly recognized in river hydraulics, thus the best way to understand them is to do measurements directly in the field. This is especially recommended for mountainous streams and rivers. However, in practice, when we suffer the lack of huge financial support (since all river measurements are unbelievably money consuming) and the lack of time for the filed work, one has to consider (using hydrological and granulometric data of the particular river reach) to use empirical formulae or approaches and with them try to asses the sediment transport intensity. In the literature focused on the sediment movement, despite some classical and well known formulae/approaches, there are many new approaches, which are well tested in the field and in hydraulic laboratories. The aim of the present paper is to present some of those approaches. Among the approaches and formulae which the reader can find here are the following approaches: DuBoys approach, Shields' approach, Egiazarow approach, Meyer-Peter and Műller approach, Bagnolds approach, Schoklitsch approach, Kalinske approach, Šamov approach, Levi approach, Einstein approach, Ackers-White'a approach, Parkers' approach, Yang's approach and finally Karim and Kennedy approach. Additionally, along the paper, the two others subjects directly connected with sediment transport are described: bed-forms, the critical velocities of the movement of sediment and no-dimensional shear stresses. Those topics are the closest to the sediment transport phenomena. It has to be said that the last publication, like the present one, was published in Poland more then the quarter of the century ago, without the second edition. From that time some new approaches were presented by scientists dealing with sediment transport phenomena and introduction of them for the audience at home seems to be interesting. Additionally in 80-ties and 90-ties of 20th century in Poland very rare, even on the world scale, radioisotope measurements of river bed-load transport took place, results of which verified the existing approaches. The present paper is addressed to all people dealing with sediment transport problems, especially to scientists, river engineers, designers and students of water environmental faculties.