Understanding and simulating the dynamics of open quantum many-body systems remain challenging due to the interplay of noise and correlations. In this seminar, we present two complementary approaches aimed at addressing these challenges. First, we introduce an optimization framework for trajectory-based stochastic methods to simulate systems with local noise. By adaptively selecting stochastic propagators to minimize average trajectory entanglement, we achieve significant reductions in the classical computational cost when using matrix product states. This strategy not only offers an exponential improvement over conventional methods but also provides insights into mixed-state entanglement measures and connects to phenomenon of measurement-induced phase transitions. Second, we turn to the problem of simulating the collective dynamics of emitter arrays near one-dimensional waveguides, a setting critical for quantum optics experiments. While tensor-network methods face limitations due to the rapid growth of correlations, we explore an alternative neural-network-based approach to overcome these challenges. This method demonstrates promise in efficiently capturing the collective dynamics, paving the way for accurate simulations in experimentally relevant regimes.