Animal detection through DNA present in environmental samples (eDNA) is a valuable tool for detecting rare species, that are difficult to observe and monitor. eDNA-based tools are underpinned by molecular evolutionary principles, which are key to devising tools to efficiently single out a targeted species from an environmental sample, using carefully chosen marker regions and customized primers. Here, we present a comprehensive review of the use of eDNA-based methods for the detection of targeted animal species, such as rare, endangered, or invasive species, through the analysis of 460 publications (2008-2022). Aquatic ecosystems have been the most surveyed, in particular, freshwaters (75%), and to a less extent marine (14%) and terrestrial systems (10%). Vertebrates, in particular, fish (38%), and endangered species, have been the most focused in these studies, and Cytb and COI are the most employed markers. Among invertebrates, assays have been mainly designed for Mollusca and Crustacea species (22%), in particular, to target invasive species, and COI has been the most employed marker. Targeted molecular approaches, in particular qPCR, have been the most adopted (73%), while eDNA metabarcoding has been rarely used to target single or few species (approx. 5%). However, less attention has been given in these studies to the effects of environmental factors on the amount of shed DNA, the differential amount of shed DNA among species, or the sensitivity of the markers developed, which may impact the design of the assays, particularly to warrant the required detection level and avoid false negatives and positives. The accuracy of the assays will also depend on the availability of genetic data from closely related species to assess both marker and primers specificity. In addition, eDNA-based assays developed for a particular species may have to be refined taking into account site-specific populations, as well as any intraspecific variation.