There are many interesting quantum phases in low-dimensions that are stable only at zero temperature.  These include topological orders and symmetry-protected topological orders in 2 and 1 spatial dimensions, respectively.  It is interesting to ask whether there exists dynamical regimes of open quantum systems where these types of order can be realized in a robust way as properties of the long-time dynamical steady state.  I will describe a partial answer to this question, showing that a variety of these orders can be stabilized against a certain type of noise (known as heralded noise).