Structuring problems for Multi-Criteria Decision Analysis (MCDA) has attracted increasing attention over the past 20 years from both a conceptual and a practical perspective. This is reflected in a significant growth in the number of published applications which use a formal approach to problem structuring in combination with an analytic method for multi-criteria analysis. The problem structuring approaches (PSMs) include general methodologies such as Checkland's Soft Systems Method (SSM), Eden and Ackermann's Strategic Options Design and Analysis (SODA) and other methods that focus on a particular aspect. We carried out a literature review that covers eight PSMs (Cognitive and Causal Maps, DPSIR, Scenario Planning, SSM, Stakeholder Analysis, Strategic Choice Approach, SODA and SWOT) and seven MCDA methods (AHP, ANP, ELECTRE, MAUT, MAVT, PROMETHEE and TOPSIS). We first identified and analysed 333 articles published during 2000-2015, then selected 68 articles covering all PSM-MCDA combinations, which were studied in detail to understand the associated processes, benefits and challenges. The three PSMs most commonly combined with MCDA are SWOT, Scenario Planning and DPSIR. AHP was by far the most commonly applied MCDA method. Combining PSMs with MCDA produces a richer view of the decision situation and enables more effective support for different phases of the decision-making process. Some limitations and challenges in combining PSMs and MCDA are also identified, most importantly relating to building a value tree and assigning criteria weights.