Compressive Sensing (CS) has become a major topic of interest in Materials Microscopy fields, promising perfect signal reconstruction with considerably fewer acquisitions.  However, we will discuss how real implementations of CS reduce the number of acquisitions by increasing the number of interactions between your probe and sample, affecting considerable sample damage.  Despite this, exploiting the sparsity of most signals captured in materials microscopy, we can design novel imaging methods which can produce high quality images while maintaining the observability of fragile specimens. The application of Machine Learning as both a post-experiment processing and pre-experiment tool will be discussed with an emphasis on Scanning Electron Microscopy and Scanning Probe Microscopy.  In addition, the ability to produce predictive scanning methods, with potentially higher signal fidelity and less sample damage, by combining image simulation with automated machine learning will be discussed.  Implications for in-situ electron microscopy will be emphasized, particularly liquid cell imaging.