While the Standard Model (SM) is extremely successful at explaining vast amounts of physical phenomena, it does not answer all of our questions. From unifying gravity to origins of dark matter, there are blatant omissions that challenge both theorists and experimentalists to venture beyond the existing theory, into the unknown worlds of exotic particles and ultra-rare phenomena. This talk will concentrate on two experimental aspects of the quest for physics beyond the SM – neutrinos and magnetic monopoles. One extremely light (at most a small fraction of eV) and another one extremely heavy (at least a fraction of TeV), these particles have fascinated physicists for decades. The first part of the talk describes one of the leading experiments to understand the nature of neutrino masses – EXO-200. It presents its latest results, current status, and discusses plans and ongoing R&D for the next generation experiment. The second part of the talk covers the ongoing search for the magnetic monopole at the LHC – the MoEDAL experiment, which recently has started the 13(14) TeV data run. Description of the motivation, the detectors, and the outlook of the experiment is given. A particular attention is paid to the potential future addition to the MoEDAL detectors – the solid state breakdown counters, which could combine threshold properties of nuclear track detectors with electronic registration in real time. Applicability of this detection technology to the future ultra large magnetic monopole searches in cosmic rays is also discussed.