Due to the lack of the viscous terms in the first-order scalar conservation laws with noise forcing, the notion of stochastic entropy solutions and renormalised entropy solutions have been introduced for the well-posedness problem. It is, however, difficult to study the vanishing noise limits (such as large deviations or averaging principles) for the stochastic entropy solutions. In this talk, we will study the kinetic solutions to the Cauchy problem for the stochastic first-order conservation laws which enable us, by utilising the weak convergence approach, to establish the Freidlin-Wentzell type large deviation principles for the first-order scalar conservation laws perturbed by small multiplicative noise. Joint work with Zhao Dong, Rangrang Zhang and Tusheng Zhang (arXiv:1806.02955v1)，to appear in Annals of Applied Probability.