We briefly describe the cosmological lithium problems followed by a summary of our recent theoretical work on the magnitude of the effects of electron screening, the possible existence of dark matter parallel universes and the use of non-extensive (Tsallis) statistics during big bang nucleosynthesis. Solutions within nuclear physics are also discussed and recent measurements of cross-sections based on indirect experimental techniques are summarized. n ↔ p p(n,γ)d d(p,γ) 3 He d(d, p)t d(d, n) 3 He 3 He(n, p)t t(d, n) 4 He 3 He(d, p) 4 He 3 He(α, γ) 7 Be t(α, γ) 7 Li 7 Be(n, p) 7 Li 7 Li(p,α) 4 He The standard BBN model predicts the 7 Li/H abundance ratio of the order of 10 −10 and the 6 Li/H abundance ratio of the order of 10 −14. Much after the BBN epoch, 6 Li and 7 Li can be produced in spallation processes by cosmic rays and 7 Li can be synthesized in novae or during AGB stars pulsations. In Ref. [6] it was reported that the 7 Li abundance is independent of the