  The goal of this overview article is to give a tangible presentation of
recent breakthrough works in discrepancy theory by M. B. Levin. These works
provide proofs for the exact lower discrepancy bounds of Halton's sequence and
a certain class of $(t, s)$-sequences. Our survey aims at highlighting the
major ideas of the proofs and we discuss further implications of the employed
methods. Moreover, we derive extensions of Levin's results.
