  A {\it vector space partition} is here a collection $\mathcal P$ of subspaces
of a finite vector space $V(n,q)$, of dimension $n$ over a finite field with
$q$ elements, with the property that every non zero vector is contained in a
unique member of $\mathcal P$. Vector space partitions relates to finite
projective planes, design theory and error correcting codes.
  In the first part of the talk I will discuss some relations between vector
space partitions and other branches of mathematics. The other part of the talk
contains a survey of known results on the type of a vector space partition,
more precisely: the theorem of Beutelspacher and Heden on
$\mathrm{T}$-partitions, rather recent results of El-Zanati et al. on the
different types that appear in the spaces V(n,2), for $n\leq8$, a result of
Heden and Lehmann on vector space partitions and maximal partial spreads
including their new necessary condition for the existence of a vector space
partition, and furthermore, I will give a theorem of Heden on the length of the
tail of a vector space partition.
  Finally, I will also give a few historical remarks.
