The physical factors relevant for the production of various low-lying Λ-hypernuclear states Λ AZ ∗ through the K − → π − and K − → π 0 reactions, in flight or from rest, on the corresponding target nuclei A Z and A ( Z + 1) are discussed, on the basis of the shell model for these nuclei and hypernuclei, together with the characteristics of the dominant γ-transitions resulting from the excited states thus produced. Detailed consideration is given for a number of hypernuclei of specific interest, including the cases of Λ 7He, Λ Li for A = 7, 9 and 10, Λ Be for A = 9 and 10, Λ B for A = 10, 11, and 12, Λ C for A = 12, 13, 14, and 15, Λ N for A = 14 and 15, and Λ 16O. The importance of (γ, π −) correlation studies for the determination of hypernuclear spin values is stressed, with the discussion of several examples.