Wavelets are the primary tool for multi scale analysis of time series data as well as of 2D images, having largely supplanted the Fourier transform in signal and image processing and analysis. There has been much recent work on extending wavelet techniques to the analysis of signals defined on graphs and complex networks. After reviewing the reasons for the shift to wavelet analysis in signal processing, we will introduce a new class of wavelet transforms on graphs, discuss some key properties this class possesses that are important for application, and as an example demonstrate their use in studying the dynamics of a cellular (phone) communications network. The talk will be aimed at non-specialists in the audience with the goal of providing an introduction to the use of these tools in applied research. The level will be informal, focusing on intuition and how the tools can be used to study biological systems (though there will be asides on the deep and rather beautiful ideas from harmonic analysis and representation theory underlying wavelets and ideas used in proofs will be mentioned for the mathematicians in the audience).