Studying correlations and dynamics in open systems is the subject of intense study. The PhD student's task is to develop analytical and numerical methods to explore the structure of dynamical correlations in open dissipative systems. On the numerical side, MPS/MPO methods shall be combined with the Chebyshev approach to extract spectral correlations. On the analytical side, third quantization methods shall be combined with diagrammatic techniques to study steady-state dynamics in infinite temperature systems.