  We review recent results obtained for a class of one-dimensional quantum
models with $1/r^2$ long-range interaction. Based on the asymptotic
Bethe-ansatz solution and conformal field theory, we study critical properties
of the continuum boson model, the SU($\nu$) spin chain, the OSp($\nu$,1)
supersymmetric {\it t-J} model, and a new hierarchy of models related to the
fractional quantum Hall effect. We further investigate the class of $1/r^2$
models with harmonic confinement by means of a newly proposed method of the
renormalized-harmonic oscillator solution.

Condensed Matter