  Strontium has proven itself to be one of the most important neutron-capture
elements in the study of metal-poor stars. Thanks to the strong absorption
lines of Sr, they can be detected even in the most metal-poor stars and also in
low-resolution spectra. However, we still cannot explain the large star-to-star
abundance scatter we derive for metal-poor stars. Here we contrast Galactic
chemical evolution (GCE) with improved abundances for SrI+II including updated
atomic data, to evaluate possible explanations for the large star-to-star
scatter at low metallicities. We derive abundances under both local
thermodynamic equilibrium (LTE) and non-LTE (NLTE) for stars spanning a large
interval of stellar parameters. Gravities and metallicities are also determined
in NLTE. We confirm that the ionisation equilibrium between SrI and SrII is
satisfied under NLTE but not LTE, where the difference between SrI and SrII is
on average ~0.3dex. We show that the NLTE corrections are of increasing
importance as the metallicity decreases. For the stars with [Fe/H]>-3 the SrI
NLTE correction is ~0.35/0.55dex in dwarfs/giants, while the Sr II NLTE
correction is +/-0.05dex. On the basis of the large NLTE corrections, SrI
should not be applied as a chemical tracer under LTE, while it is a good tracer
under NLTE. SrII is a good tracer under both LTE and NLTE (down to [Fe/H]\sim
-3), and LTE is a safe assumption for this majority species. However, the Sr
abundance from SrII lines is dependent on an accurate surface gravity
determination, which can be obtained from NLTE spectroscopy of Fe lines or from
parallax measurements. We could not explain the star-to-star scatter (which
remains under both LTE and NLTE) by the use of the GCE model, since the Sr
yields to date are too uncertain to draw firm conclusions. At least two
production sites seem necessary in order to account for this large scatter
(abridged).
