The recently developed hierarchical equations of motion(HEOM)method is employed to study the dynamics,as well as linear and nonlinear spectra of molecular aggregates in photosynthetic systems.A brief introduction of the theoretical method and its application is first presented to show that,it is important to go beyond the commonly used second order perturbation approximation in the so called intermediate coupling regime.We will then focus on the recent developments in calculating the emission and pump-probe spectra,where arriving at the correct excited state equilibrium structure,and capturing the correct dynamics are both important.We will also present recent works on applying the HEOM method effectively to general form of spectral densities,which opens the way to simulate a broad range of problems in condensed phase dynamics and spectroscopy.