Wicked sustainability problems (WSPs) are an important and particularly challenging type of problem. Science and engineering education can play an important role in preparing students to deal with such problems, but current educational practice may not adequately prepare students to do so. We address this gap by providing insights related to students' abilities to address WSPs. Specifically, we aim to (I) describe key constituents of engineering students' approaches to a WSP, (II) evaluate these approaches in relation to the normative context of education for sustainable development (ESD), and (III) identify relevant aspects of learning related to WSPs. Aim I is addressed through a phenomenographic study, while aims II and III are addressed by relating the results to research literature about human problem solving, sustainable development, and ESD. We describe four qualitatively different ways of approaching a specific WSP, as the outcome of the phenomenographic study: A. "Simplify and avoid," B. "Divide and control," C. "Isolate and succumb," and D. "Integrate and balance." We identify approach D as the most appropriate approach in the context of ESD, while A and C are not. On this basis, we identify three learning objectives related to students' abilities to address WSPs: learn to use a fully integrative approach, distinguish WSPs from tame and well-structured problems, and understand and consider the normative context of SD. Finally, we provide recommendations for how these learning objectives can be used to guide the design of science and engineering educational activities.