This chapter studies in depth, both from a model- and a proof-theoretic perspective, various logics in the so-called “strict-tolerant” family. We provide results of Inferential and Metainferential Soundness and Completeness. We analyze the local, global and absolute global st-ranges of the relevant calculi, relative to the set of all trivaluations for the language. We explain the well-known relationship between the metainferences and inferences valid in st- and tt-consequence relations, respectively. Finally, we show that the strict-tolerant phenomenon generalizes to every non-trivial Tarskian logic. Most of the contents of this chapter are known to the literature. Some of them, however, are either new or correct some (small) mistakes in other articles.