Heavy flavour physics, as one of the most important parts in the standard model (SM), plays important roles in testing the SM and probing the effects of new physics beyond SM. Thanks to the two B factories, Beijing spectrometer (BES) and large hadron collider beauty (LHCb) experiment, in the past decades, there is great development in heavy flavour physics, in both experimental and theoretical sides. In heavy flavour physics, the first work is to test SM by measuring three angles ($\alpha$, $\beta$ and $\gamma$) and sides of Cabbibo-Kobayashi-Maskawa (CKM) triangle. Though the current results are in agreement with SM, the fit becomes less constrained in the presence of new physics, and ${\cal~O}(20%$) contributions of new physics are still allowed. The charge conjugation and parity (CP) asymmetries measured by two B factories helped us to study the matter-antimatter asymmetry in the Universe, and the discovered CP asymmetry in $\rm~B\to~K_s~J/\psi$ had led to the nobel prize for Kobayashi and Maskawa. In addition, the mass differences between the neutral meson and their own anti-meson can present us the information of the scale of the new physics, because possible new particles might contribute to $\rm~D^0$, $\rm~B_d^0$, and $\rm~B_s^0$ meson mixing through box diagrams. The nonleptonic decays of B mesons afford us a new plate for studying the quantum chromodynamics (QCD) and factorization concept, as well as searching for the strong phases, which are important factors in CP asymmetries. Importantly, the rare decays induced by the flavour-changing neutral-current has attracted much interest, because the new physics can affect the observables remarkably through penguin diagrams. In addition, it is of interest to note that the recent anomalies, such as $R_{\rm~K^{(*)}}$, $R({\rm~D}^{(*)})$ and $P_5^\prime$, might be the hints of new physics beyond SM. In order to explain these anomalies, many models have been proposed, however, all of them should be further tested in the future on both experimental and theoretical sides. Moreover, heavy flavor physics also provides us an important plate for studying the new exotic states. Many new discovered exotic states in BES-III, B factories and LHCb, such as $\rm~X(3872)$, $\rm~Z_c(3900)$ and $\rm~P_c(4450,4380)$, motivate us to further study the quark model and QCD. In 2018, Belle-II will take data, where the total luminosity is predicted to be $50\rm~ab^{-1}$ and $10^{10}$ B meson pair could be produced. The proposed International Linear Collider, Circular Electron-Positron Collider and Hyper-Z Factory, can also produce large number of B mesons, as well as $\rm~B_s$, $\rm~B_c$ and $\Lambda_b$, when the collision energy is set to be ${\cal~O}(m_Z)$. These high precision or energy machines, together with the current LHCb experiment and its next generation, will lead heavy flavor physics to a new golden era.
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