  CRESST is a multi-stage experiment directly searching for dark matter (DM)
using cryogenic $\mathrm{CaWO_4}$ crystals. Previous stages established leading
limits for the spin-independent DM-nucleon cross section down to DM-particle
masses $m_\mathrm{DM}$ below $1\,\mathrm{GeV/c^2}$. Furthermore, CRESST
performed a dedicated search for dark photons (DP) which excludes new parameter
space between DP masses $m_\mathrm{DP}$ of $300\,\mathrm{eV/c^2}$ to
$700\,\mathrm{eV/c^2}$.
  In this contribution we will discuss the latest results based on the previous
CRESST-II phase 2 and we will report on the status of the current CRESST-III
phase 1: in this stage we have been operating 10 upgraded detectors with
$24,\mathrm{g}$ target mass each and enhanced detector performance since summer
2016. The improved detector design in terms of background suppression and
reduction of the detection threshold will be discussed with respect to the
previous stage. We will conclude with an outlook on the potential of the next
stage, CRESST-III phase 2.
