We present results from our recent investigations on detectors comprising cascaded gas electron multipliers (GEM) and cascaded GEMs with micro-hole and strip (MHSP) electrodes. We discuss the factors governing the operation of these fast radiation imaging detectors, that have single-charge sensitivity. The issue of ion-backflow and ion-induced secondary effects is discussed in some detail, presenting ways for its reduction and suppression. Applications are presented in the fields of photon imaging in the UV-to-visible spectral range as well as x-ray and neutron imaging.