To a metric space X one can associate its Roe algebra C*(X), a
noncommutative algebra which is meant to in encode the large-scale (or
'coarse') geometry of the space.  I will introduce these ideas and
discuss some applications to 'classical' geometry and topology, which
follow if the Roe algebra is genuinely a 'good model' for X.   I will
then discuss how much information about the space X one can expect to
recover from its Roe algebra in general (this last part is joint work
with Ján Špakula).