  Let $G$ be a simple algebraic group over an algebraically closed field $k$ of
characteristic $p$. The classification of the conjugacy classes of unipotent
elements of $G(k)$ and nilpotent orbits of $G$ on $\operatorname{Lie}(G)$ is
well-established. One knows there are representatives of every unipotent class
as a product of root group elements and every nilpotent orbit as a sum of root
elements. We give explicit representatives in terms of a Chevalley basis for
the eminent classes. A unipotent (resp. nilpotent) element is said to be
eminent if it is not contained in any subsystem subgroup (resp. subalgebra), or
a natural generalisation if $G$ is of type $D_n$. From these representatives,
it is straightforward to generate representatives for any given class. Along
the way we also prove recognition theorems for identifying both the unipotent
classes and nilpotent orbits of exceptional algebraic groups.
