  The recent data from the Boomerang and MAXIMA-1 balloon flights have marked
the beginning of the precision era of Cosmic Microwave Background anisotropy
(CMB) measurements. We investigate the observational constraints from the
current CMB anisotropy measurements on the simplest inflation models,
characterized by a single scalar field $\phi$, in the parameter space
consisting of scalar spectral index $n_S$ and tensor/scalar ratio $r$. If we
include constraints on the baryon density from big bang nucleosynthesis (BBN),
we show that the favored inflationary models have negligible tensor amplitude
and a ``red'' tilt, with a best fit of $n_S \simeq 0.93$, which is consistent
with the simplest ``small-field'' inflation models, but rules out large-field
models at the $1\sigma$ level. Without including BBN constraints, a broader
range of models are consistent with the data. The best fit (assuming negligible
reionization) is a scale-invariant spectrum, $n_S \simeq 1$, which includes
large-field and hybrid scenarios. Large-field models (such as chaotic and
power-law inflation) with tilt $n_S < 0.9$ are strongly disfavored in all
cases.
