  Let p be prime. A noncommutative p-solenoid is the C*-algebra of Z[1/p] x
Z[1/p] twisted by a multiplier of that group, where Z[1/p] is the additive
subgroup of the field Q of rational numbers whose denominators are powers of p.
In this paper, we survey our classification of these C*-algebras up to
*-isomorphism in terms of the multipliers on Z[1/p], using techniques from
noncommutative topology. Our work relies in part on writing these C*-algebras
as direct limits of rotation algebras, i.e. twisted group C*-algebras of the
group Z^2 thereby providing a mean for computing the K-theory of the
noncommutative solenoids, as well as the range of the trace on the K_0 groups.
We also establish a necessary and sufficient condition for the simplicity of
the noncommutative solenoids. Then, using the computation of the trace on K_0,
we discuss two different ways of constructing projective modules over the
noncommutative solenoids.
