Mycotoxins are a major threat to animal and human health, as well as to the global feed supply chain. Among them, aflatoxins, fumonisins, zearalenone, T-2 toxins, deoxynivalenol, and Alternaria toxins are the most common mycotoxins found in animal feed, with genotoxic, cytotoxic, carcinogenic, and mutagenic effects that concern the animal industry. The chronic negative effects of mycotoxins on animal health and production and the negative economic impact on the livestock industry make it crucial to develop and implement solutions to mitigate mycotoxins. In this review, we summarize the current knowledge of the mycotoxicosis effect in livestock animals as a result of their contaminated diet. In addition, we discuss the potential of five promising phytogenics (curcumin, silymarin, grape pomace, olive pomace, and orange peel extracts) with demonstrated positive effects on animal performance and health, to present them as potential anti-mycotoxin solutions. We describe the composition and the main promising characteristics of these bioactive compounds that can exert beneficial effects on animal health and performance, and how these phytogenic feed additives can help to alleviate mycotoxins’ deleterious effects.