A sensitive measurement of parity-violating (PV) observables in few-nucleon systems can shed light on our current understanding of the hadronic weak interaction at low momentum transfers. Theoretical models describe the nucleon-nucleon weak interaction at low energies with 6 parameters that need, in principle, to be determined in the same number of independent experiments. In this context, a series of experiments with cold neutrons are being proposed and developed. Particularly, experiments that aim to measure the parity-violating asymmetry in the distribution of the gamma-rays emitted in the capture of polarized neutrons by protons and deuterium, will be discussed in this paper.