In this review we discuss the present status of strange nuclear physics, with special attention to the weak decay of Λ-hypernuclei. The models proposed for the evaluation of the Λ decay widths are summarized and their results are compared with the data. The rates Γ N M =Γ n +Γ p (+Γ 2 ), Γ π 0 and Γ π - are well explained by several calculations. Despite the intensive investigations of the last years, the main open problem remains a sound theoretical interpretation of the large experimental values of the ratio Γ n /Γ p . However, the large uncertainties involved in the experimental determination of the ratio do not allow to reach any definitive conclusion. The Γ n /Γ p puzzle is strongly related to the so-called ΔI=1/2 rule on the isospin change in the non-mesonic decay, whose possible violation cannot be established at present, again due to the insufficient precision of the data. Although recent works offer a step forward in the solution of the puzzle, further efforts (especially on the experimental side) must be invested in order to understand the detailed dynamics of the non-mesonic decay. Even if, by means of single nucleon spectra measurements, the error bars on Γ n /Γ p have been considerably reduced very recently at KEK (however, with central data compatible with older experiments), a clean extraction of Γ n /Γ p is needed. What is missing at present, but planned for the next future, are measurements of (1) nucleon energy spectra in double coincidence and (2) nucleon angular correlations: such observations allow to disentangle the nucleons produced in one- and two-body induced decays and lead to a direct determination of Γ n /Γ p . Notably, the two-body component of the non-mesonic decay rates has not been measured yet, due to the too low counting rates expected for a coincidence experiment. For the asymmetric non-mesonic decay of polarized hypernuclei the situation is even more puzzling. Indeed, strong inconsistencies appear already among data. A recent experiment obtained a positive intrinsic Λ asymmetry parameter, a Λ , for Λ 5 He. This is in complete disagreement with a previous measurement, which obtained a large and negative a Λ for p-shell hypernuclei, and with theory, which predicts a negative value moderately dependent on nuclear structure effects. Also in this case, improved experiment establishing with certainty the sign and magnitude of a Λ for s- and p-shell hypernuclei will provide a guidance for a deeper understanding of hypernuclear dynamics and decay mechanisms.