This chapter covers the fundamental and applied aspects of the motion of isolated spherical and nonspherical particles in Newtonian and Non-Newtonian fluids. The discussion is aimed at describing the underlying physical process in flouncing hydrodynamic drag, wave characteristics, settling velocity, effect of confining wall, etc. for a sphere in Newtonian, power-law, and viscoplastic fluids. This discussion is then extended to the case of nonspherical particles by introducing additional shape factors like sphericity, equal volume, sphere diameter, etc. Naturally, the terminal falling velocity of nonspherical particles in a stationary fluid cannot be predicted as reliably as that of a sphere. Including here is also a brief section on the analogous problem of a fluid sphere-drop and bubble pertaining to the law Reynolds number regime. This chapter is concluded by considering the accelerating motion of a particle in the gravitational field. The applicability of the ideas presented in this chapter has been illustrated through solved examples.