CARMENES is an echelle spectrograph with two arms, one in the visible and one in the infrared, mounted on the 3.5 m telescope in Calar Alto Observatory, Spain. Since 2016, the CARMENES guaranteed observing time program has conducted a radial-velocity survey of 365 M dwarfs in search for planetary companions. However, over the past three years CARMENES has also devoted a substantial amount of time to follow up TESS transiting planet candidates around M dwarfs. By design, the TESS mission is particularly well-suited to provide such exciting candidates around the brightest and nearest M dwarfs. These planets, particularly those in the habitable zone of their host stars, constitute the bulk of warm and temperate worlds amenable for detailed atmospheric characterization with current and future ground- and space-based facilities. The CARMENES-TESS program has already validated and characterized a large number of interesting planetary systems (including for example GJ357, GJ486 and GJ732), some of which have already been included in the approved GTO and Cycle 1 GO programs for JWST. In this talk we will quickly review the past discoveries of our program, and introduce the latest results. These include several new rocky planets, 3 of them within 10 parsecs from Earth, which places them among the best known rocky worlds for atmospheric studies with JWST, and several temperate sub-giant planets.