Abstract: The square-lattice t-J model is considered as a basic paradigm for understanding strong correlation effects and unconventional superconductivity (SC), which has attracted intense theoretical studies. I will review recent progress in computational studies of such model systems based on large-scale density matrix renormalization group (DMRG) simulations. I will also present a global phase diagram for extended t-J model to demonstrate the general emergence of unconventional SC. In particular, a uniform d-wave SC is the ground state for both electron and hole doped t-J model with small nearest neighbor hopping and spin couplings, while a d-wave and pairing density wave co-existing SC phase emerges for the pure t-J model (with only nearest neighbor couplings) intertwining spin and charge orders. These results enrich theoretical understanding of cuprate superconductors.