Peanuts are the seeds of a legume crop grown for nuts and oil production. Peanut allergy has gained significant attention as a public health issue due to its increasing prevalence, high rate of sensitization, severity of the corresponding allergic symptoms, cross-reactivity with other food allergens, and lifelong persistence. Given the importance of peanuts in several sectors, and taking into consideration the criticality of their high allergic potential, strategies aiming at mitigating their allergenicity are urgently needed. In this regard, most of the processing methods used to treat peanuts are categorized as either thermal or thermomechanical techniques. The purpose of this review is to provide the reader with an updated outlook of the peanut’s allergens, their mechanisms of action, the processing methods as applied to whole peanuts, as well as a critical insight on their impact on the allergenicity. The methods discussed include boiling, roasting/baking, microwaving, ultrasonication, frying, and high-pressure steaming/autoclaving. Their effectiveness in alleviating the allergenicity, and their capacity in preserving the structural integrity of the treated peanuts, were thoroughly explored. Research data on this matter may open further perspectives for future relevant investigation ultimately aiming at producing hypoallergenic peanuts.