Research results about the movement and accumulation of floating marine debris drifting throughout the world's oceans are reviewed in this paper. A mechanism for this accumulation and movement is strongly associated with surface currents consisting of the Ekman drift and the geostrophic current, because all floating marine debris is passive to surface currents. The basic published mechanism for the North Pacific is common across the world's ocean. After marine debris accumulates in the narrow Ekman convergence zone, it is moved to the east by geostrophic currents. The most important thing is that floating marine debris concentrates in some specific regions, independent of the initial quantity of marine debris. In order to resolve this problem and to avoid an asbestos-like problem, the use of biodegradable polymers is important in our daily life.