  A vector space partition $\mathcal{P}$ in $\mathbb{F}_q^v$ is a set of
subspaces such that every $1$-dimensional subspace of $\mathbb{F}_q^v$ is
contained in exactly one element of $\mathcal{P}$. Replacing "every point" by
"every $t$-dimensional subspace", we generalize this notion to vector space
$t$-partitions and study their properties. There is a close connection to
subspace codes and some problems are even interesting and unsolved for the set
case $q=1$.
