Quenched disorder, in the sense of random imperfections in a system, is both a blessing and a curse for scientists — it can give rise to a host of novel phenomena, but it also tends to impede transport and communication. Here we cover examples of both from our work on quantum dynamics, motivated primarily by proposals for quantum computing and quantum information protocols. In the first part, we discuss tunneling processes in “rugged energy landscapes”, of which the classic optimization problems from computer science (such as Traveling Salesman and Satisfiability) are examples. After describing how many such problems share essential features with mean-field spin glasses — long-range interactions, disorder, frustration — we summarize our understanding of the quantum dynamical phases in the latter. In the second part, we consider the opposite extreme of 1D nearest-neighbor spin chains. We describe how “Lieb-Robinson bounds” have proven to be an invaluable tool for studying both many-body dynamics and constraints on quantum information protocols. We then cover our recent work developing Lieb-Robinson bounds tailored to disordered spin chains.