  Sign problem in quantum Monte Carlo (QMC) simulation appears to be an
extremely hard yet interesting problem. In this article, we present a
pedagogical overview on the origin of the sign problem in various quantum Monte
Carlo simulation techniques, ranging from the world-line and stochastic series
expansion Monte Carlo for boson and spin systems to the determinant and
momentum-space quantum Monte Carlo for interacting fermions. We point out the
basis dependency of the sign problem and summarize the progresses to cure, ease
and even make use of the sign problem over the years, such as symmetry analysis
of the underlying Hamiltonian, basis optimization in writting down the
partition functions and many others. Moreover, we state that although
traditional lore saying that in case of sign problem, the average sign in QMC
simulation approaches zero exponentially fast with the space-time volume of the
configurational space, there are recent breakthroughs showing this is not
always the case and based on the properties of the partition function for
finite size systems, one could distinguish when the average sign has the usual
exponential scaling and when it is bestowed with an algebraic scaling at the
low temperature limit. Fermionic QMC simulations with such algebraic sign
problems have been successfully carried out for extended Hubbard-type and
quantum Moir\'e lattice models.
