If Shor‘s celebrated algorithm can be efficiently implemented on existing quantum computers, cryptography  and everything in our IT security infrastructure based on it (almost everything)  is broken. Hence we need alternatives to these techniques. Lattice-based cryptography is probably the most promising alternative to present cryptography. However, the effect of quantum computing on lattice-based crypto is not well understood, neither in the mid- nor long-term perspective. I will review the reasons we believe that lattice-based crypto may be less susceptible to quantum algorithms than traditional crypto. I will also outline research questions and directions to better understand the effect of quantum computing on the complexity of lattice problems and lattice-based crypto.