Electron microscopes are advanced scientific instruments that use electrons instead of light to examine objects on a very fine scale. In this lecture, I will describe how modern electron microscopes work and I will give examples of the contribution that electron microscopy has made to our knowledge of the world. In the first part of the talk, I will show how the use of better electron lenses and sophisticated software have recently improved our ability to obtain quantitative information about the local microstructure and chemistry of nanoscale crystals and low-dimensional materials at the atomic scale. I will then show how we can image electromagnetic fields inside materials with sub-5-nm spatial resolution and why this information is important in microelectronics, geology and biology. I will conclude with a personal perspective on directions for the future development of transmission electron microscopy. Such developments may ultimately lead to the ability to measure the positions, chemical identities and magnetic moments of individual atoms in a material in three dimensions.