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The existence of massive black holes (MBHs) was postulated in the 1960s, when the first quasars were discovered. In the late 1990s their reality was proven beyond doubt in the Milky way and a handful nearby galaxies. Since then, enormous theoretical and observational efforts have been made to understand the astrophysics of MBHs. We have discovered that some of the most massive black holes known, weighing billions of solar masses, powered luminous quasars within the first billion years of the Universe. The first MBHs must therefore have formed around the time the first stars and galaxies formed. Dynamical evidence also indicates that black holes with masses of millions to billions of solar masses ordinarily dwell in the centers of today's galaxies. MBHs populate galaxy centers today, and shone as quasars in the past; the quiescent black holes that we detect now in nearby bulges are the dormant remnants of this fiery past. In this review we report on basic, but critical, questions regarding the cosmological significance of MBHs. What physical mechanisms led to the formation of the first MBHs? How massive were the initial MBH seeds? When and where did they form? How is the growth of black holes linked to that of their host galaxy? The answers to most of these questions are works in progress, in the spirit of these reports on progress in physics. [ABSTRACT FROM AUTHOR]