Being competitive in the international agri-food trade is an important aim of every country. It should be noted that this term has neither a commonly accepted definition nor a synthetized index to quantify it. The most commonly used indices in the international literature are the Balassa index and its modified versions (revealed trade advantage, revealed competitiveness, normalized revealed comparative advantage, and revealed symmetric comparative advantage) and different export and/or import-related indices (e.g., the Grubel–Lloyd index or the trade balance index). Based on a systematic review of the literature, these measurements were identified along with the major factors suggested for higher agri-food trade competitiveness. It seems that supportive legislation and/or (trade) policy is the most crucial factor, followed by higher value-added/more sophisticated goods, and high, efficient, and profitable production. Although the EU and its member states were overrepresented in the analyzed literature, the candidate countries, as well as other important trading partners of the EU, e.g., Canada, China, or the ASEAN countries, were also analyzed. Thus, some of these findings may be generalized.