Aerospace structures are thin-walled shell structures whose load-bearing capacity is often limited by buckling phenomena. The application of variable angle tow (VAT) composites allows to increase the buckling resistance by tailoring the fiber paths. Fiber placement technologies such as automated fiber placement and continuous tow shearing for VAT composites have been improved enormously in recent years. However, induced material and geometric uncertainties from the manufacturing process have a major influence on the structural performance. The paper focuses on appropriate uncertainty quantification for VAT composites, selecting various uncertainty models based on available data. Different uncertainty models are introduced to quantify the natural variability (aleatory uncertainty) and lack of knowledge (epistemic uncertainty). An uncertain fiber path definition with fuzzy variables is presented to model fiber path deviations. In addition, geometric imperfections are modeled as random fields and as Fourier series to analyze the imperfection sensitivity. Based on this, a design optimization of VAT composites is performed in presence of uncertainties. The introduced methods are demonstrated on a VAT composite panel and a cylindrical shell. Geometric imperfection measurements are provided for the VAT composite cylindrical shell to validate the approach based on experimental results. This paper contributes to a better understanding of uncertainties of tow-steered structures. The results reveal a potential conflict in optimizing the robustness measures (e.g. minimizing the variation of the buckling loads) and enhancing the performance measures (e.g. maximizing the mean value of the buckling loads) visualized by Pareto fronts. This emphasizes the need to consider uncertainties in a design process of VAT composite shells based on multi-objective optimization.