Abstract. Publications of recent years dealing with laboratory experiments of immersion freezing reveal uncertainties about the fundamentals of heterogeneous freezing nucleation. While it appears well accepted that there are two major factors that determine the process, namely fluctuations in the size and configuration of incipient embryos of the solid phase and the role of the substrate to aid embryo formation, views have been evolving about the relative importance of these two elements. The importance of specific surface sites is being established in a growing number of experiments and a number of approaches have been proposed to incorporate these results into model descriptions. Many of these models share a common conceptual basis yet diverge in the way random and deterministic factors are combined. The divergence can be traced to uncertainty about the permanence of nucleating sites, to the lack of detailed knowledge about what surface features constitute nucleating sites, and to the consequent need to rely on empirical or parametric formulas to define the population of sites of different effectiveness. Recent experiments and models, consistent with earlier work, demonstrate the existence and primary role of permanent nucleating sites and the continued need for empirically based formulations of heterogeneous freezing. In order to clarify some aspects of the processes controlling immersion freezing, the paper focuses on three identifiably separate but interrelated issues: (i) the combination of singular and stochastic factors, (ii) the role of specific surface sites, and (iii) the modeling of heterogeneous ice nucleation.