The combination of the high intensity proton beam facilities and massive detectors for precision measurements of neutrino oscillation parameters including the charge-parity violating (CPV) phase will open the door to help make beyond the standard model (BSM) physics reachable even in low energy regimes in the accelerator-based experiments. Large-mass detectors with highly precise tracking and energy measurements, excellent timing resolution, and low energy thresholds will enable the searches for BSM phenomena from cosmogenic origin, as well. Therefore, it is also conceivable that BSM topics in the next-generation neutrino experiments could be the dominant physics topics in the foreseeable future, as the precision of the neutrino oscillation parameter and CPV measurements continue to improve.This paper provides a review of the current landscape of BSM theory in neutrino experiments in two selected areas of the BSM topics-dark matter and neutrino related BSM-and summarizes the current results from existing neutrino experiments to set benchmarks for both theory and experiment. This paper then provides a review of upcoming neutrino experiments throughout the next 10 to 15 year time scale and their capabilities to set the foundation for potential reach in BSM physics in the two aforementioned themes. An important outcome of this paper is to ensure theoretical and simulation tools exist to carry out studies of these new areas of physics, from the first day of the experiments, such as Deep Underground Neutrino Experiment in the U.S. and Hyper-Kamiokande Experiment in Japan.