  We discuss recently introduced numerical linked-cluster (NLC) algorithms that
allow one to obtain temperature-dependent properties of quantum lattice models,
in the thermodynamic limit, from exact diagonalization of finite clusters. We
present studies of thermodynamic observables for spin models on square,
triangular, and kagome lattices. Results for several choices of clusters and
extrapolations methods, that accelerate the convergence of NLC, are presented.
We also include a comparison of NLC results with those obtained from exact
analytical expressions (where available), high-temperature expansions (HTE),
exact diagonalization (ED) of finite periodic systems, and quantum Monte Carlo
simulations.For many models and properties NLC results are substantially more
accurate than HTE and ED.
