Astrophysical neutron capture reactions in the slow s-process or rapid r-process produce essentially all nuclides heavier than iron. We pursue experiments aimed at measuring in the laboratory the cross section of such reactions in conditions mimicking the stellar s-process. A Liquid-Lithium Target (LiLiT) bombarded by the high-power (2-3 kW) proton beam at Soreq Applied Research Accelerator Facility (SARAF, Soreq NRC, Israel) produces an intense neutron yield (3-5×1010 n/s) having a 30-keV quasi- Maxwellian flux spectrum, well suited for the s-process regime. We will describe experiments in which the reaction products are detected by α-, β-, γ-spectrometry or atom counting. While the r-process cannot at present be directly probed in the laboratory, the search for live r-process radioactive species, and in particular actinides, deposited on Earth by the interstellar wind, provides interesting experimental clues. Ultra-high sensitivity experiments using the technique of accelerator mass spectrometry (AMS) in samples from deep-sea terrestrial archives point to a rarity of interstellar r- process 244Pu(81 My), incompatible with the rate of Galactic core-collapse supernovae. On the other hand, clear time-resolved signals of 60Fe(2.6 My) globally deposited on Earth are observed.