One of the main challenges in organizing the efficient development of modern aircraft during the conceptual design phase is the provision of methodological support for a complex, iterative process of synthesizing and selecting design solutions under uncertainty. Uncertainty is the primary cause of unforeseen violations of critical constraints and errors in the determination of objective function values. At the same time, during the conceptual design phase, the main parameters and characteristics that define the overall appearance of the aircraft are selected. Failure to adequately consider uncertainty in computational and optimization tasks often results in uncompetitive and impractical design solutions. In recent years, there has been a growing number of studies aimed at addressing this issue by adapting traditional, deterministic models and algorithms to accommodate inaccurate input data. The article discusses the methods that are used to synthesize and select design solutions for aircraft design under uncertainty. At the same time, the main focus is on the latest achievements in statistical and intelligent computing, which reduce the time and increase the information content of the conceptual design stage. Approaches to dealing with parameter uncertainty, solving the problem of target uncertainty, and surrogate modeling to reduce computational costs are presented. The main provisions and conclusions presented in the framework of the review study are illustrated by examples from the world scientific literature.