In-flight aircraft icing is a serious problem affecting flight safety and operational reliability. Atmospheric supercooled water droplets impinge on aircraft surfaces and freeze, forming ice, which can severely degrade aerodynamic performance and operational safety, potentially leading to a complete loss of control. Computational fluid dynamics is an important tool in the development of aircraft anti-icing systems, and modeling icing processes is a complex, interdisciplinary, and multifactorial task. This talk aims to discuss approaches to describing the air-droplet incoming flow in aircraft icing modeling, as well as the behavior of droplets interacting with an ice-covered aerodynamic surface. The Navier-Stokes equations are used to describe the motion of the carrier medium. The applicability of the polydisperse Eulerian, Lagrangian trajectory, and homogeneous models is analyzed for supercooled droplet dynamics. Numerical simulation of icing processes is performed using the control volume method, taking into account the conservation laws of mass, momentum, and energy, as well as microphysical processes observed in previous experimental studies. The analysis conducted in this work showed that the homogeneous model is appropriate for conditions near the phase transition point. The freezing of moisture that impinges on the aerodynamic surface is primarily governed by the temperature of the aerodynamic body and its heat exchange with the incoming flow. In cases where supercooled atmospheric droplets play a dominant role in the icing process, the Lagrangian trajectory model and the polydisperse Eulerian model are preferable for describing the air-droplet flow. The main conclusion of the work is the preference for the use of the polydisperse Eulerian model, as it best accounts for the characteristics of two-phase viscous compressible flow around bodies and the interaction of the carrier and liquid phases, making it the most promising approach for modeling aircraft icing. When describing the interaction of supercooled droplets with an aerodynamic surface, one must consider the mechanism of liquid movement along the ice surface through “jumping”, “splashing”, and the transport of rebounded droplets, which subsequently settle. This paper demonstrates the proposed approach using a test case and compares it with known experimental data. The results obtained can be used to ensure flight safety, design anti-icing systems, and investigate aviation accidents.