In this talk I will give an overview of some recent results on singular SPDEs, especially on the dynamical $\Phi^4_d$ model. On the one hand, some results based on strong approach, i.e. regularity structure and paracontrolled distribution method are given. On the other hand, I will present some results based on weak approach,i.e. energy solutions and Dirichlet form approach. At last I will present some open problems in this field.

Zhu Rongchan, obtained doctor degree from  Chinese Academy of Sciences and the University of Bielefeld, Germany in 2012. She is currently an associate professor at Beijing Institute of Technology. Her research interest is SPDEs, especially on singular SPDEs.   In 2019, she won the Excellent Youth Fund Project from NSFC.