We focused on high resolution measurements of spin noise at low magnetic fields, showing how one can obtain information about spin relaxation from the spontaneous spin noise resonance width. Most recently, we have demonstrated a new phenomenon related to spin-exchange collisions, namely that in a multi-species atomic vapor and low magnetic fields, spin-exchange collisions induce positive inter-species spin-noise correlations. This is an extension in the realm of quantum fluctuations of the well known property of spin exchange, the inter-species transfer of a deterministic spin polarization. The new effect, termed spin-noise exchange, was revealed by a low-field increase of the total spin-noise power.