Several different types of parameterization of heterogeneous ice nucleation for cloud and climate models have been developed over the past decades, ranging from empirically-derived expressions to parameterizations of ice crystal nucleation rates derived from theory (including the parameterization developed by the authors, hereafter referred to as KC). Parameterizations schemes that address the deliquescence-freezing (DF), which combines the thermodynamically indistinguishable modes of condensation freezing and immersion freezing, are assessed here in the context of thermodynamic constraints, laboratory measurements, and recent field measurements. It is shown that empirical schemes depending only on the ice saturation ratio or only on temperature can produce reasonable crystal concentrations, but ice crystal nucleation is thermodynamically prohibited in certain regions of the temperature-saturation ratio phase space. Some recent empirical parameterizations are shown to have insufficient efficiency, yielding clouds that are almost entire liquid at temperatures as low as −35 °C. A reasonable performance of the KC ice nucleation scheme is demonstrated by comparison with data from several recent field campaigns, laboratory data, climatology of cloud phase-state, and GCM parameterizations. Several mis-applications of the KC parameterization that appeared recently in the literature are described and corrected, by emphasizing that a correct application of the KC scheme with simultaneous dependence on the temperature and saturation ratio requires integration of the individual nucleation rates over the measured size spectrum of the environmental aerosol, and not over the spectrum of ice nuclei equal to the crystal concentration at the exit of an experimental device. Simulation with a spectral bin model and correct application of KC scheme adequately describes ice nucleation via the DF mode and yields crystal concentrations and phase state close to those measured in the single-layer stratocumulus cloud observed in the Mixed Phase Arctic Cloud Experiment (MPACE). An assessment of some deficiencies in current parcel modeling methods and cloud chamber observations and their impact on parameterization development and evaluation is provided.