Pyrochlore oxides with chemical formula of A2B2O7 exhibit a diverse range of electronic properties as a representative family of quantum materials. These properties mostly stem from strong electron correlations at the transition metal B site and typical geometrical frustration effects on the pyrochlore lattice. Furthermore, the coupling between the magnetic moments of the rare-earth A site and the conduction electrons at the B site, along with the relativistic spin-orbit coupling particularly affecting the 4d/5d electrons at the B site, gives rise to the topological characteristics of the correlated electrons. This review paper focuses on the metal-insulator transitions in pyrochlore oxides as evidence of the strong electron correlation, which is highlighted as a rich source of intriguing charge dynamics coupled with frustrated spin-orbital entangled magnetism.