Algebraic topologists have traditionally addressed the question "what is the shape of a topological space?". In more recent times, computational topologists have turned their attention to the question "what is the shape of a data set?". Unfortunately it is not enough simply to transplant the methods of algebraic topology into C++ or MATLAB code; noise and sampling irregularities present in real data sets cause serious instability in the operations used to estimate topology. Happily, multiscale methods come to the rescue. By introducing a scale parameter, and applying a bit of clever algebra, one can stabilise the calculations and obtain reliable topological estimates. I will survey the work of several researchers in this area.
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