Newly born and young radio sources are in a delicate phase of their life. Their jets are fighting their way through the surrounding gaseous medium, strongly experiencing this interaction while, at the same time, impacting and affecting the interstellar medium (ISM). Quantifying this interplay has far reaching implications: the rate of occurrence and the magnitude of the interaction between radio jets and ISM can have consequences for the evolution of the host galaxy. Despite the hostile conditions, cold gas - neutral atomic hydrogen and molecular - has been often found in these objects and can be also associated to fast outflows. Here we present the results from two studies of H I and molecular gas illustrating what can be learned from these phases of the gas. We first describe a statistical study of the occurrence and kinematics of H I observed in absorption with the Westerbork Synthesis Radio telescope. This allows a comparison between the properties of the gas in extended and in compact/young radio sources. The study shows that the young radio sources not only have an higher detection rate of H I, but also systematically broader and more asymmetric H I profiles, most of them blueshifted. This supports the idea that we are looking at young radio jets making their way through the surrounding ISM, which also appears to be, on average, richer in gas than in evolved radio sources. Signatures of the impact of the jet are seen in the kinematics of the gas, but the resulting outflows may be characteristic of only the initial phase of the radio source evolution. However, even among the young sources, we identify a population that remains undetected in H I even after stacking their profiles. Orientation effects can only partly explain the result. These objects either are genuinely gas-poor or have different conditions of the medium, e.g. higher spin temperature. The upcoming blind H I surveys which are about to start with large-field-of-view radio facilities (i.e. Apertif at the WSRT and ASKAP) will allow us to expand the statistics and reach even higher sensitivity with stacking techniques. We further present the case of the radio source IC 5063 where we have used the molecular gas observed with ALMA to trace in detail the jet impacting the ISM. The kinematics of the cold, molecular gas co-spatial with the radio plasma shows this process in action. The ALMA data reveal a fast outflow of molecular gas extending along the entire radio jet (˜1 kpc), with the highest outflow velocities at the location of the brighter hot-spot. The results can be described by a scenario of a radio plasma jet expanding into a clumpy medium, interacting directly with the clouds and inflating a cocoon that drives a lateral outflow into the ISM. This is consistent with the scenario proposed by numerical simulations for the expansion of a young radio jet, confirming the disruptive effect the radio plasma jet can have. Following this case, more ALMA observations of nearby young radio sources will be able to confirm if this process is common, as expected, in the initial phase of the evolution of the radio source.