The electrochemical behaviors of molybdenum and its oxides, both in bulk and thin film dimensions, are critical because of their widespread applications in steels, electrocatalysts, electrochromic materials, batteries, sensors, and solar cells. An important area of current interest is electrodeposited CIGS-based solar cells where a molybdenum/glass electrode forms the back contact. Surprisingly, the basic electrochemistry of molybdenum and its oxides has not been reviewed with due attention. In this Review, we assess the scattered information. The potential and pH dependent active, passive, and transpassive behaviors of molybdenum in aqueous media are explained. The major surface oxide species observed, reversible redox transitions of the surface oxides, pseudocapacitance and catalytic reduction are discussed along with carefully conducted experimental results on a typical molybdenum glass back contact employed in CIGS-based solar cells. The applications of molybdenum oxides and the electrodeposition of molybdenum are briefly reviewed.