We update the constraints on the fraction of the Universe going into
primordial black holes (PBHs) over the mass range $10^{-5}$--$10^{50}$ g. Those
smaller than $\sim 10^{15}$ g would have evaporated by now due to Hawking
radiation, so their abundance at formation is constrained by the effects of
evaporated particles on big bang nucleosynthesis, the cosmic microwave
background (CMB), the Galactic and extragalactic $\gamma$-ray and cosmic ray
backgrounds and the possible generation of stable Planck mass relics. PBHs
larger than $\sim 10^{15}$ g are subject to a variety of constraints associated
with gravitational lensing, dynamical effects, influence on large-scale
structure, accretion and gravitational waves. We discuss the constraints on
both the initial collapse fraction and the current fraction of the cold dark
matter in PBHs at each mass scale but stress that many of the constraints are
associated with observational or theoretical uncertainties and some are no
longer applicable. We also consider indirect constraints associated with the
amplitude of the primordial density fluctuations, such as second-order tensor
perturbations and $\mu$-distortions arising from the effect of acoustic
reheating on the CMB, but these only apply if PBHs are created from the
high-$\sigma$ peaks of nearly Gaussian fluctuations. Finally we discuss how the
constraints are modified if the PBHs have an extended mass function, this being
relevant if PBHs provide some combination of the dark matter, the LIGO/Virgo
coalescences and the seeds for cosmic structure.