  Given a point set $P \subseteq X$ of size $n$ in a metric space $(X,dist)$ of
doubling dimension $d$ and two parameters $k \in N$ and $z \in N$, the
$k$-center problem with $z$ outliers asks to return a set $C^\ast \subseteq X$
of $k$ centers such that the maximum distance of all but $z$ points of $P$ to
their nearest center in $C^\ast$ is minimized. An $(\epsilon,k,z)$-coreset for
this problem is a weighted point set $P^*$ such that an optimal solution for
the $k$-center problem with $z$ outliers on $P^*$ gives a
$(1\pm\epsilon)$-approximation for the $k$-center problem with $z$ outliers on
$P$. We study the construction of such coresets in the Massively Parallel
Computing (MPC) model, and in the insertion-only as well as the fully dynamic
streaming model. We obtain the following results, for any given $0 < \epsilon
\le 1$: In all cases, the size of the computed coreset is $O(k/\epsilon^d+z)$.
  - In the MPC model, we present a deterministic $2$-round and a randomized
$1$-round algorithm. Additionally, we provide a deterministic algorithm that
obtains a trade-off between the number of rounds, $R$, and the storage per
machine.
  - For the insertion-only streaming model, we present an algorithm and a tight
lower bound to support it.
  - We also discuss the dynamic streaming model, which allows both insertions
and deletions in the data stream. In this model, we present the first algorithm
and a lower bound.
  - Finally, we consider the sliding window model, where we are interested in
maintaining an $(\epsilon,k,z)$-coreset for the last $W$ points in the stream,
we present a tight lower bound that confirms the optimality of the previous
work by De Berg, Monemizadeh, and Zhong (ESA2020).
