Simulations of non-equilibrium dynamics is essential for understanding the quantum transport of charge, energy and spins in extended systems such as chains and rings. The most common simulation methods like density matrix renormalization group [1,2] utilize tensor networks [3] to mitigate the exponential growth of computational complexity with system size. Such simulations are typically done under the assumption that the extended system is isolated. However, this is very clearly an approximation. The phonons in the system can often provide a dissipative medium that modulates the dynamics. To go beyond perturbative treatments, one has to often resort to simulations. However, the non-perturbative tensor network methods fail to accurately account for the presence of thermal dissipative media [4]. Methods based on path integrals are especially convenient when dealing with the static and dynamic effects of these dissipative media [5]. Such path integral methods proceed via integrating the bath out and creating so-called influence functionals [6]. We have recently developed a tensor network method that is able to rigorously incorporate the bath effects in terms of its Feynman-Vernon influence functional [7] while being able to handle the full Hilbert space of these extended systems with relative ease. I will discuss this method and illustrate applications on the study of electronic energy transport and absorption spectra of photosynthetic complexes [8], and exploration of effect of temperature gradients on the non-equilibrium dynamics [9].