Radioactive atoms and molecules are unique systems that allow us to investigate physics phenomena within and beyond the Standard Model. Possessing a large sensitivity to violations of the fundamental symmetries of nature, certain molecules can be engineered to answer some of the biggest open questions in physics, such as the origin of the matter-antimatter asymmetry and the nature of Dark Matter. Radioactive molecules containing octupole-deformed nuclei, such as radium monofluoride (RaF), are expected to be particularly sensitive to symmetry-violating nuclear properties and can probe energy scales beyond hundreds of TeV. In this talk, I will present pioneering results in the study of radioactive molecules obtained from a series of laser spectroscopy experiments performed on short-lived RaF molecules at the ISOLDE facility at CERN. These measurements allowed us to establish a highly effective laser cooling scheme for these molecules and to observe, for the first time, the effects of minuscule electroweak nuclear effects on the molecular energy levels. These results opened the way for future precision studies and new physics searches using radioactive molecules. In the second half of my talk, I will discuss ongoing efforts in developing new laser spectroscopy experiments to further our understanding of how quantum chromodynamics (QCD) can be used to describe emerging nuclear phenomena and the properties of extreme neutron-rich matter, such as neutron stars. I will present the status of a novel experiment aiming to measure parity-violating nucleon-nucleon weak interactions using molecular ions inside a Penning trap. The method is expected to provide enhancements in the sensitivity to the sought-for signals of more than 12 orders of magnitude compared to atoms. Finally, I will present the development of a highly sensitive experimental setup for precision laser spectroscopy studies of very short-lived isotopes (lifetime < 10 ms), expected to be produced in the future at existing radioactive beam facilities worldwide.  Such nuclear systems are of paramount importance to guide our understanding of nuclear matter and electroweak nuclear properties.