  We study the Popular Matching problem in multiple models, where the
preferences of the agents in the instance may change or may be
unknown/uncertain. In particular, we study an Uncertainty model, where each
agent has a possible set of preferences, a Multilayer model, where there are
layers of preference profiles, a Robust model, where any agent may move some
other agents up or down some places in his preference list and an Aggregated
Preference model, where votes are summed over multiple instances with different
preferences.
  We study both one-sided and two-sided preferences in bipartite graphs. In the
one-sided model, we show that all our problems can be solved in polynomial time
by utilizing the structure of popular matchings. We also obtain nice structural
results. With two-sided preferences, we show that all four above models lead to
NP-hard questions for popular matchings. By utilizing the connection between
dominant matchings and stable matchings, we show that in the robust and
uncertainty model, a certainly dominant matching in all possible prefernce
profiles can be found in polynomial-time, whereas in the multilayer and
aggregated models, the problem remains NP-hard for dominant matchings too.
  We also answer an open question about $d$-robust stable matchings.
