In the current post-antibiotic era, botanicals represent one of the most employed nutritional strategies to sustain antibiotic-free and no-antibiotic-ever production. Botanicals can be classified either as plant extracts, meaning the direct products derived by extraction from the raw plant materials (essential oils (EO) and oleoresins (OR)), or as nature-identical compounds (NIC), such as the chemically synthesised counterparts of the pure bioactive compounds of EO/OR. In the literature, differences between the use of EO/OR or NIC are often unclear, so it is difficult to attribute certain effects to specific bioactive compounds. The aim of the present review was to provide an overview of the effects exerted by botanicals on the health status and growth performance of poultry and pigs, focusing attention on those studies where only NIC were employed or those where the composition of the EO/OR was defined. In particular, phenolic compounds (apigenin, quercetin, curcumin and resveratrol), organosulfur compounds (allicin), terpenes (eugenol, thymol, carvacrol, capsaicin and artemisinin) and aldehydes (cinnamaldehyde and vanillin) were considered. These molecules have different properties such as antimicrobial (including antibacterial, antifungal, antiviral and antiprotozoal), anti-inflammatory, antioxidant, immunomodulatory, as well as the improvement of intestinal morphology and integrity of the intestinal mucosa. The use of NIC allows us to properly combine pure compounds, according to the target to achieve. Thus, they represent a promising non-antibiotic tool to allow better intestinal health and a general health status, thereby leading to improved growth performance.