I will discuss some new constructions of p-adic distributions and measures on compact unitary groups and cohomological representations of GL_n over CM fields (in the ordinary setting, interpolating in anticyclotomic towers). These constructions fit naturally into the rubrik of calculations leading to the nonvanishing theorems of Cornut and Vatsal for the special case of n=2, as well as to certain Euler/Kolyvagin system constructions, as I will explain.