Advances in optics and detectors for electrons enable new investigations of electron physics and quantum imaging techniques at the nanoscale. For example, nanoscale diffraction holograms can be used to coherently sculpt free electron wavefunctions with non-trivial spatial and momentum distributions that provide new ways to probe interactions, optical excitations, and coherence. Holographic apertures can be used as efficient beamsplitters for implementing versatile interferometric scanning transmission electron microscopy (STEM). For example, STEM holography provides a way to directly image electron phase shifts by recording the interference between two separate STEM probes is recorded. An electron interferometer built with two beamsplitters provides discrete outputs, enabling a way to probe the coherence and symmetry of nano-optical excitations, as well as other quantum processes. We describe and experiment by which electrons in superpositions of isolated paths can excite the same optical transition in a nanoplasmonic structure, albeit from different positions. Despite this strong inelastic interaction with a specimen, we find that these two paths still interfere and that the excitation of a plasmon introduces a relative π phase shift between the two probes. In another set of experiments, we use the same set up to demonstrate interaction-free measurements, a type of quantum counterfactual measurement protocol in which the presence of an object can be detected without a probing particle interacting with it. These techniques provide a new way to explore how electrons interact with nanosystems and can potentially reduce the electron dose required to image objects in the TEM. Combining these technologies with ultrafast electron techniques will provide unprecedented spatiotemporal control of electrons, enabling a new age of advanced electron microscopy.