Fuzzy systems perform approximate reasoning using imprecisely described if-then rules. Fuzzy rule interpolation (FRI) facilitates such reasoning when carried out on incomplete or sparse rule bases, where certain observations may not match any existing rules. Traditional fuzzy rule-based inference requires at least partial direct pattern matching between observations and the given rules; FRI, instead, reasons through manipulation of rules that bear similarity with an unmatched observation. FRI techniques have been extensively investigated for decades, resulting in a wide range of approaches with successful applications. This talk will focus on a popular group of techniques called Transformation-based FRI (T-FRI), which rely on exploiting linear transformations of automatically selected rules nearest to an unmatched observation. This talk will first provide a review of the underlying, seminal T-FRI approach, followed by a brief introduction to a family of methods, including: adaptive T-FRI, backward T-FRI, higher-order T-FRI, dynamic T-FRI and weighted T-FRI, each of which addresses some of the critical limitations of the original. Then, the talk will present real-world applications that solve challenging problems like network security and medical diagnosis. Finally, the talk will conclude with several initial sketches for further development in this important area.