Noise is the most serious obstacle to developing quantum computers. This article reviews two recently published results that answer the essential questions on noisy quantum circuits in particular meaningful situations expected in the near future. The purpose of the article is not to provide comprehensive surveys but to introduce how to apply some essential state-of-the-art techniques to the simulation and verification of noisy quantum circuits. The first part reveals that even slight noise at the end of computation spoils the quantum advantage under a particular noise model. This raises the question of verifying that a given quantum circuit is not significantly affected by noise. The second part shows an efficient verification method of a given quantum circuit with the help of a smaller verified quantum circuit when the circuit to be verified is sparse and shallow.