Covering: 2000 to 2019 According to a 2012 survey from the Centers for Disease Control and Prevention, approximately 18% of the U.S. population uses natural products (including plant-based or botanical preparations) for treatment or prevention of disease. The use of plant-based medicines is even more prevalent in developing countries, where for many they constitute the primary health care modality. Proponents of the medicinal use of natural product mixtures often claim that they are more effective than purified compounds due to beneficial "synergistic" interactions. A less-discussed phenomenon, antagonism, in which effects of active constituents are masked by other compounds in a complex mixture, also occurs in natural product mixtures. Synergy and antagonism are notoriously difficult to study in a rigorous fashion, particularly given that natural products chemistry research methodology is typically devoted to reducing complexity and identifying single active constituents for drug development. This report represents a critical review with commentary about the current state of the scientific literature as it relates to studying combination effects (including both synergy and antagonism) in natural product extracts. We provide particular emphasis on analytical and Big Data approaches for identifying synergistic or antagonistic combinations and elucidating the mechanisms that underlie their interactions. Specific case studies of botanicals in which synergistic interactions have been documented are also discussed. The topic of synergy is important given that consumer use of botanical natural products and associated safety concerns continue to garner attention by the public and the media. Guidance by the natural products community is needed to provide strategies for effective evaluation of safety and toxicity of botanical mixtures and to drive discovery in botanical natural product research.