It remains an open problem whether the 3D incompressible Euler equations can develop finite-time singularity from smooth initial data in the whole space. In this talk, I will review some most recent results on finite-time blowups with self-similar features, divided into three parts. In the first part, I will talk about the dynamic rescaling method for establishing asymptotically self-similar finite-time blowup with rigorous computer-assisted proof. In the second part, I will introduce the constructions of exact self-similar blowup solutions for some simple models of the 3D Euler equations based on the fixed-point method. In the last part, I will talk about recent findings on potential self-similar finite-time blowups of the 3D Euler equations with multi-scale features, which are closely related to traveling wave solutions and may provide a new approach towards Euler singularity.