At present, there are a variety of different approaches to the targeted regulation of gene expression. However, most approaches are devoted to the activation of gene transcription, and the methods for gene silencing are much fewer in number. In this review, we describe the main systems used for the targeted suppression of gene expression (including RNA interference (RNAi), chimeric transcription factors, chimeric zinc finger proteins, transcription activator-like effectors (TALEs)-based repressors, optogenetic tools, and CRISPR/Cas-based repressors) and their application in eukaryotes—plants and animals. We consider the advantages and disadvantages of each approach, compare their effectiveness, and discuss the peculiarities of their usage in plant and animal organisms. This review will be useful for researchers in the field of gene transcription suppression and will allow them to choose the optimal method for suppressing the expression of the gene of interest depending on the research object.