The hycean paradigm in the search for life elsewhere Atmospheric characterisation of habitable-zone exoplanets is a major frontier of exoplanet science. The detection of atmospheric signatures of habitable Earth-like exoplanets is challenging due to their small planet-star size contrast and thin atmospheres with high mean molecular weight. Recently, a new class of habitable sub-Neptune exoplanets, called Hycean worlds, has been proposed. Hycean worlds are planets with H2-rich atmospheres and planet-wide oceans with thermodynamic conditions similar to those in the Earth's oceans. Their large sizes and extended atmospheres, compared to rocky planets of the same mass, make Hycean worlds significantly more accessible to atmospheric spectroscopy. Recently, we reported the first JWST spectrum of a candidate Hycean world, K2-18 b, with detections of multiple carbon-bearing molecules in its atmosphere. In this talk, we will present the latest observational and theoretical advances in the characterisation of candidate Hycean worlds made possible by high-precision JWST spectroscopy. We will discuss inferences of the atmospheric chemical compositions, temperature structure, clouds/hazes, atmospheric extent, chemical disequilibrium and the possibility of a habitable ocean underneath the atmosphere. Our findings demonstrate the unprecedented potential of JWST for characterising Hycean worlds, and temperate sub-Neptunes in general, and open a new era of atmospheric characterisation of habitable-zone exoplanets with JWST.