Human gene expression is regulated by thousands of proteins that can activate or repress transcription. To predict and control gene expression, we need to know where in the protein their effector domains are, and how strongly they activate or repress. To systematically measure the function of transcriptional effector domains in human cells, we developed a high- throughput assay in which pooled libraries of thousands of domains are recruited individually to a reporter gene. Cells are then separated by reporter expression level, and the library of protein domains is sequenced to determine the frequency of each domain in silenced versus active cell populations. We used this method to: 1) quantify the activation, silencing, and epigenetic memory capability of all nuclear protein domains annotated in Pfam, including the KRAB family of >300 domains. We find that while evolutionary young KRABs are strong repressors, some of the old KRABs are activators. 2) characterize the amino acids responsible for effector function via deep mutational scanning. We applied it to the KRAB used in CRISPRi to map the co-repressor binding surface and identify substitutions that improve stability, silencing, and epigenetic memory. 3) discover novel functional domains in unannotated regions of large transcription factors, including repressors as short as 10 amino acids. Together, these results provide a resource of 600 human proteins containing effectors, and demonstrate a scalable strategy for assigning functions to protein domains.