  A submanifold $\phi:M\to \mathbb E^{m}$ is called {\it biharmonic} if it
satisfies $\Delta^{2}\phi=0$ identically, according to the author. On the other
hand, G.-Y. Jiang studied biharmonic maps between Riemannian manifolds as
critical points of the bienergy functional, and proved that biharmonic maps
$\varphi$ are characterized by vanishing of bitension $\tau_{2}$ of $\varphi$.
During last three decades there has been a growing interest in the theory of
biharmonic submanifolds and biharmonic maps.
  The study of $H$-submanifolds of $\mathbb E^{m}$ were derived from biharmonic
submanifolds by only requiring the vanishing of the tangential component of
$\Delta^{2}\phi$. In 2014, R. Caddeo et. al. named a submanifold $M$ in any
Riemannian manifold ``biconservative'' if the stress-energy tensor $\hat S_{2}$
of bienergy satisfies ${\rm div}\, \hat S_{2}=0$. Caddeo et. al. also shown
that a Euclidean submanifolds is an $H$-submanifold if and only if the
tangential component of $\tau_{2}$ vanishes and hence the notions of
$H$-submanifolds and of biconservative submanifolds coincide for Euclidean
submanifolds.
  The first results on biconservative hypersurfaces were proved by T. Hasanis
and T. Vlachos, where they called such hypersurfaces {\it H-hypersurfaces} in
1995. Since then biconservative submanifolds has attracted many researchers and
a lot of interesting results were obtained. The aim of this article is to
provide a comprehensive survey on recent developments on biconservative
submanifolds done most during the last decade.
