The tempered Lefschetz thimble method (TLTM) [arXiv:1703.00861] is a parallel-tempering algorithm towards solving the numerical sign problem. It uses the flow time of the antiholomorphic gradient flow as a tempering parameter, and is expected to tame both the sign and ergodicity problems simultaneously that exist intrinsically in thimble methods. In this talk, we elaborate on the basics of TLTM, and apply the method to various problems, including the (0+1)-dimensional finite-density Thirring model and the quantum Monte Carlo simulation of the Hubbard model away from half filling.