The complexity of the hardware architectures of modern supercomputers led the community of developers of scientific libraries to adopt new parallel programming paradigms. Among them, task-based programming has certainly become one of the most popular as it allows for high productivity while ensuring high performance and portability by delegating tasks management to a runtime system. In this talk, we will present an overview of sparse solvers that have been designed in the context of the Matrices Over Runtime Systems @ Exascale (MORSE) and Solvers for Heterogeneous Architectures (SOLHAR) projects. We will present the design of new direct solvers implementing supernodal (PaStiX) and multifrontal (qr-mumps) methods, new Krylov solvers ensuring pipelining both at a numerical and software level, new sparse hybrid methods (MaPHyS) as well as data sparse libraries implementing fast multipole methods (ScalFMM) and hierarchical matrices (hmat, in collaboration with Airbus Group Innovations). For all these methods, we will highlight the challenges we have faced in terms of expressivity, granularity, scheduling and scalability and illustrate their performance on large academic and industrial test problems.