A diversity of experimental techniques has been developed over the last 25 years to create samples of molecular gases at temperatures close to the Absolute Zero—here we consider samples in the range from 10s of Kelvin (cold) down to 10s of nanoKelvin (ultracold). In these exotic physical environments, a range of novel experiments can be conducted which bring high levels of control over the properties of these ‘almost stationary’ molecules, in some cases with control over single trapped molecules achievable. In this article, recent advances in this field since 2020, both in terms of the ability to produce and manipulate the molecules and understand their properties, and also in the development of new applications of these technologies, are highlighted. Applications include observing explicit ‘quantum effects’ in chemical reactivity, developing an understanding of chemistry in cold astrophysical media, the creation of exotic phases of matter, the use of trapped molecules in quantum computation and simulations systems, and the use of very high-precision spectroscopic measurements to answer fundamental physics questions beyond the standard model of particle physics.