The neutron's unique properties enable high measurement precision at extremely low energies, making it a well suited probe to search for diluted traces of physics that dominated the very early Universe. In the next few years a boost in statistical quality of experiments by more than two orders of magnitude is expected by super-thermal sources of ultra-cold neutrons (UCN) at various facilities. A prominent experiment using UCN is the search for the neutron’s electric dipole moment (EDM) using spin-clock comparisons combined with Ramsey’s method of separated oscillatory fields. Such an EDM would be a manifestation of yet unknown broken symmetries above the TeV scale and an important ingredient to explain the matter-antimatter asymmetry in the Universe in most theories beyond the SM. An example of a related technological development is the magnetic environment, providing the world's smallest existing magnetic field over a large volume. Another scientific highlight is the realization of a gravity-resonance spectroscopy technique, a first step towards a Ramsey-like experiment without electromagnetic interactions. Here, quantized states of neutrons confined by gravity have transitions excited by vibrating mirrors. These experiments benefit from the small charge radius of the neutron that conceptually gives access to effects occurring at short distances, e.g. new gravity-like forces or spin-matter couplings. In addition to an overview of this field of research, I will discuss selected recent developments with potentially large impact, once the new facilities are available.