Tensor network methods have been widely used in exploring the intricacies of quantum many-body physics. In this proposal, our primary focus will be on a specialized variant of tensor network methods known as continuous tensor network methods. This approach not only proves highly advantageous for simulating continuous systems but also extends its applicability to the temporal dimension of quantum lattice systems, facilitating the computation of thermodynamic properties within those systems. Despite the promising potential demonstrated by continuous tensor network methods, they are still in their early stages compared to conventional tensor network methods. In this proposal, we aim to delve deeper into the development and applications of continuous tensor network techniques for simulating quantum many-body physics. This research encompasses the application of continuous matrix product states as variational states for targeting the low-energy physics of multi-component Bose gasses, as well as their use in the temporal direction for computing thermodynamic and transport properties of low-dimensional quantum lattice systems.