  In this talk I review the proposal to formulate quantum field theories (QFTs)
on a Lefschetz thimble, which was put forward to enable Monte Carlo simulations
of lattice QFTs affected by sign problem. First I will review the theoretical
justification of the approach, and comment on some open issues. Then, I will
review the algorithms that have been proposed and are being tested to represent
and simulate a lattice QFT on a Lefschetz thimble. In particular, I will review
the lessons from the very first models of QFTs that have been studied with this
approach.
