The fraction of baryons in the Universe, as inferred from both measurements of 
light element ratios combined with predictions by big-bang nucleosynthesis 
models, and temperature fluctuations of the cosmic microwave background, 
amount to only (4.6 ± 0.4) % of the total matter/energy budget.
Most of these baryons are observed in the intergalactic medium at redshift >
~2, in the so called Ly-alpha forest. However, at z<2 only half of these 
baryons are actually observed in stars, galaxies, hot virialized gas in 
clusters of galaxies, residual Ly-alpha forest and shock-heated OVI gas at 
temperatures of about 1e5 K. About 54 % of the baryons are missing.

Recent measurements, performed through X-ray and UV spectroscopy of the local 
intergalactic medium, suggest that these 'missing baryons' are hiding in a 
filamentary web of hot and tenuous intergalactic matter (the WHIM), at 
temperatures of about 1e6 K and densities of ~ 1e-5 cm-3, so confirming 
hydrodynamical simulations predictions for the formation of structures in the 
Universe.

In this paper I will first review the current observational evidence for the 
existence of this medium, and present the first estimates of the cosmological 
mass density of baryons in the OVII WHIM filaments.
Then I will discuss the future lines of research for WHIM studies, with 
particular emphasis on (a) identifying the most promising observational 
strategies with current X-ray and UV spectrometers, to dramatically reduce the 
uncertainties on the estimate of Omega_b(WHIM) and dN/dz(WHIM), and (b) 
defining some of the possible rich fields of studies related to the WHIM that 
will be enabled by future X-ray spectroscopic satellites in the next two 
decades (e.g. determination of the cosmological parameters through WHIM 
density fluctuations, Universe ecology, dark-matter concentration maps, etc.).