We first briefly review existing solvers for the generalized Riemann problem (GRPm), i.e., the Cauchy problem for hyperbolic systems with polynomial initial data of degree m, including source terms. These solvers constitute the fundamental building blocks of ADER methods, which achieve arbitrary accuracy of order m+1in both space and time. ADER schemes are one-step, nonlinear, fully discrete methods and can be formulated within both the finite volume and discontinuous Galerkin finite element frameworks. We then focus on a particular approach for solving the GRPm: the time-reconstruction method, originally introduced by Dematté et al. [1] for scalar problems. After revisiting the scalar case, we provide a detailed extension of the method to nonlinear hyperbolic systems. It is shown that the resulting solver significantly simplifies the ADER methodology compared to other existing approaches, such as those based on Cauchy–Kovalevskaya procedures. The presentation concludes with a series of numerical test problems demonstrating that the proposed methods are orders of magnitude more efficient than low-order schemes. Here, efficiency is defined as the computational cost required by a given scheme to achieve a prescribed small error.