Herpesviruses are important pathogens that can cause significant morbidity and mortality in the human population. Herpesviruses have a double-stranded DNA genome, and viral genome replication takes place inside the nucleus. Upon entering the nucleus, herpesviruses have to overcome the obstacle of cellular proteins in order to enable viral gene expression and genome replication. In this review, we want to highlight cellular proteins that sense incoming viral genomes of the DNA-damage repair (DDR) pathway and of PML-nuclear bodies (PML-NBs) that all can act as antiviral restriction factors within the first hours after the viral genome is released into the nucleus. We show the function and significance of both nuclear DNA sensors, the DDR and PML-NBs, and demonstrate for three human herpesviruses of the alpha-, beta- and gamma-subfamilies, HSV-1, HCMV and KSHV respectively, how viral tegument proteins antagonize these pathways.