We introduce novel time discretization schemes for coupled systems of partial differential equations. Our main focus is systems that are defined over spatially distinct domains with a common interface, where the coupling is enforced. We also look at volume coupled models defined over the same domain. Fluid-structure Interactions are one type of important application problem that fall into this framework. Each of the physical problems can be governed by a different type of equations and therefore can exhibit different dynamics. In traditional methods, the time-step size has to be the same for both of the systems and adjusted to the subproblem with faster dynamics. As a result, the time-step size in the other one is unnecessarily small. Our aim is to develop time discretization schemes allowing for different time-step sizes without violating the coupling conditions. We introduce a hierarchy of time meshes - a common uniform coarse mesh and a second, finer mesh that can be chosen independently. The problems are formulated within the space-time framework which allows us access to the apparatus usually reserved for space discretization only. Although the formulation is monolithic, we solve the systems sequentially relying on a partitioned approach. To resolve the coupling conditions, special decoupling algorithms are introduced. Two such algorithms are discussed, namely a relaxation and a shooting method. We further develop an a posteriori error estimator based on the Dual Weighted Residual method and define the necessary adjoint formulations needed for this approach. The estimator is then used as an adaptivity criterion. We numerically test the performance of both of the decoupling strategies as well as the error estimator for a series of test problems. We further expand our results by proving theoretical estimates and show error estimates for the implicit Euler time-stepping scheme. The starting point consists of a simple system of ordinary differential equations. It is then followed by the analysis of two heat equations coupled across a common interface scaled by different diffusivity constants. As the final problem, we look at an analogous Stokes equations system. We study both semi-discrete as well as fully discrete cases. For the Stokes problem, the estimates are proved in a special newly defined norm that incorporates the coupling conditions.