  A submanifold $M$ of a Euclidean $m$-space is said to be biharmonic if
$\Delta \overrightarrow H=0$ holds identically, where $\overrightarrow H$ is
the mean curvature vector field and $\Delta$ is the Laplacian on $M$. In 1991,
the author conjectured that every biharmonic submanifold of a Euclidean space
is minimal. The study of biharmonic submanifolds is nowadays a very active
research subject. In particular, since 2000 biharmonic submanifolds have been
receiving a growing attention and have become a popular subject of study with
many progresses.
  In this article, we provide a brief survey on recent developments concerning
my original conjecture and generalized biharmonic conjectures. At the end of
this article, I present two modified conjectures related with biharmonic
submanifolds.
