An upper semicontinuous complex Finsler metric $F: T^{1,0}M\rightarrow \mathbb{R}^+$ on a complex manifold $M$ is called strongly pseudoconvex (resp. strongly convex) if its indicatrix $I_F(p)=\{F(p;v)<1|v\in T_pM\}$ is strongly pseudoconvex (resp. strongly convex) at each point $p\in M$ . The well-known Kobayashi metrics on strongly convex bounded domains with smooth boundary in $\mathbb{C}^n$ provides us with such examples. In this talk, I shall first recall some basic notions of complex Finsler metrics and then introduce some recent results we obtained on strongly pseudoconvex (resp. strongly convex) complex Finsler manifolds, as well as complex Finsler-Einstein vector bundles in the sense of Aikou. Partially are jonit work with Hongchuan Xia and Liling Sun.