In the first part of this talk, using the examples of Ising, XY, and quantum Bose-Hubbard models, I shall explain some basic ingredients in worm-type Monte Carlo algorithms for classical and quantum lattice models of which the configuration space can be represented in terms of closed paths or flows. The second part of the talk shall discuss two applications for the classical and the quantum cases, respectively. Hereby, I shall particularly spend some effort on describing how the high-precision Monte Carlo data near quantum critical point can be used to study quantum dynamics via analytical continuation--e.g., observation of universal properties of Higgs resonance and conductivity, of which the latter can be used to test the AdS/CFT correspondence.

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