In this talk, we present integrable two-component CH-type models with peakon and weak kink solutions. The two-component model is proven integrable through its Lax pair and infinitely many conservation laws. Moreover, we investigate the interaction of multi-peakons and interplaying of weak-kink with peakons for two-component models. We will also discuss reductions from two-component models and amazing solutions, such as nontraveling type of peakons, weak-kink-peakons, and rogue peakons. In particular, we first time propose weak-kink solutions, rogue peakon solutions, and weak-kink-peakon interaction solutions [1, 2, 3]. Those results are joint work with my collaborator Dr. Baoqiang Xia and Dr. Ruguang Zhou.