To combat viral infections, plants possess innate and adaptive immune pathways, such as RNA silencing, R gene and recessive gene-mediated resistance mechanisms. However, it is likely that additional cell-intrinsic restriction factors (CIRF) are also involved in limiting plant virus replication. This review discusses novel CIRFs with antiviral functions, many of them RNA-binding proteins or affecting the RNA binding activities of viral replication proteins. The CIRFs against tombusviruses have been identified in yeast (Saccharomyces cerevisiae), which is developed as an advanced model organism. Grouping of the identified CIRFs based on their known cellular functions and subcellular localization in yeast reveals that TBSV replication is limited by a wide variety of host gene functions. Yeast proteins with the highest connectivity in the network map include the well-characterized Xrn1p 5’-3’ exoribonuclease, Act1p actin protein and Cse4p centromere protein. The protein network map also reveals an important interplay between the pro-viral Hsp70 cellular chaperone and the antiviral co-chaperones, and possibly key roles for the ribosomal or ribosome-associated factors. We discuss the antiviral functions of selected CIRFs, such as the RNA binding nucleolin, ribonucleases, WW-domain proteins, single- and multi-domain cyclophilins, TPR-domain co-chaperones and cellular ion pumps. These restriction factors frequently target the RNA-binding region in the viral replication proteins, thus interfering with the recruitment of the viral RNA for replication and the assembly of the membrane-bound viral replicase. Although many of the characterized CIRFs act directly against TBSV, we propose that the TPR-domain co-chaperones function as guardians of the cellular Hsp70 chaperone system, which is subverted efficiently by TBSV for viral replicase assembly in the absence of the TPR-domain co-chaperones.