Isogeometric analysis (IGA) [1] employs splines and their generalizations, such as NURBS, as basis functions for numerical simulations. This choice facilitates the integration of numerical simulation with computer-aided geometric design, furthermore offering superior accuracy compared to traditional finite element methods (FEM) based on C0 or discontinuous piecewise polynomial functions, due to the ap proximation properties of splines. Given these advantages in spatial discretization, a natural question arises: why not extend this approach to the time domain and approximate the time dependence of solutions of evolutionary partial differential equations (PDEs) using splines? The computational viability of spline-based temporal discretization crucially depends on the develop ment of efficient and, ideally, parallel solvers. In [2], we proposed a class of solvers that exploit the tensor-product structure of spline spaces, achieving high computational efficiency through tensor linear algebra techniques. This presentation will discuss the use of space-time isogeometric analysis for hyperbolic PDEs, discussing its advantages, limitations, and practical implications. REFERENCES [1] J Austin Cottrell, Thomas JR Hughes, and Yuri Bazilevs. Isogeometric Analysis: toward integration of CAD and FEA. John Wiley & Sons, 2009. [2]Sara Fraschini Gabriele Loli, Andrea Moiola, Giancarlo Sangalli. An unconditionally stable space-time isogeometric method for the acoustic wave equation. CAMWA, 2024.