Toxin-antitoxin (TA) systems are a large group of small genetic modules found in prokaryotes and their mobile genetic elements. Type II TAs are encoded as bicistronic (two-gene) operons that encode two proteins: a toxin and a neutralizing antitoxin. Using our tool NetFlax (standing for Network-FlaGs for toxins and antitoxins), we have performed a large-scale bioinformatic analysis of proteinaceous TAs, revealing interconnected clusters constituting a core network of TA-like gene pairs. To understand the structural basis of toxin neutralization by antitoxins, we have predicted the structures of 3,419 complexes with AlphaFold2. Together with mutagenesis and functional assays, our structural predictions provide insights into the neutralizing mechanism of the hyperpromiscuous Panacea antitoxin domain. In antitoxins composed of standalone Panacea, the domain mediates direct toxin neutralization, while in multidomain antitoxins the neutralization is mediated by other domains, such as PAD1, Phd-C, and ZFD. We hypothesize that Panacea acts as a sensor that regulates TA activation. We have experimentally validated 16 NetFlax TA systems and used domain annotations and metabolic labeling assays to predict their potential mechanisms of toxicity (such as membrane disruption, and inhibition of cell division or protein synthesis) as well as biological functions (such as antiphage defense). We have validated the antiphage activity of a RosmerTA system encoded by Gordonia phage Kita, and used fluorescence microscopy to confirm its predicted membrane-depolarizing activity. The interactive version of the NetFlax TA network that includes structural predictions can be accessed at http://netflax.webflags.se/ .