Markov Chain Monte Carlo methods can provide statistically exact solutions to some many-body quantum problems. Two examples are particles confined to one dimension and bosonic particles. However, for most "important" problems, it is not known whether Monte Carlo methods can be used to provide exact solutions. Two examples that I will discuss are 1) can Monte Carlo methods solve general many-fermion systems, such as those involving electrons? 2) can Monte Carlo methods provide information about how a quantum system will respond to a distubance? This problem can be reduced to continuing noisy data from imaginary time to real time, or equivalently performing an inverse Laplace transform on noisy data. Bayesian and maximum entropy methods are often used to do this.