  We review recent progress in the field of cold trapped molecular ions. A new
generation of collision and cold chemistry experiments between atoms and ions
has emerged, where cold atoms and ions are brought into contact in a controlled
way in novel hybrid atom-ion platforms. Furthermore, new possibilities for the
preparation and detection of molecular quantum states with high sensitivity and
precision have been demonstrated based on quantum-logic schemes. These advances
represent important stepping stones for new directions in fundamental research
and technological applications across various domains including precision
measurements, quantum technologies and chemical dynamics.
