  A Ricci soliton $(M^n,g,v,\lambda)$ on a Riemannian manifold $(M^n,g)$ is
said to have concurrent potential field if its potential field $v$ is a
concurrent vector field.
  In the first part of this paper we completely classify Ricci solitons with
concurrent potential fields. In the second part we derive a necessary and
sufficient condition for a submanifold to be a Ricci soliton in a Riemannian
manifold equipped with a concurrent vector field. In the last part, we classify
shrinking Ricci solitons with $\lambda=1$ on Euclidean hypersurfaces.
  Several applications of our results are also presented.
