Machine learning and artificial intelligence (ML/AI) are rapidly becoming an indispensable part of physics research, with domain applications ranging from theory and materials prediction to high-throughput data analysis. In parallel, the recent successes in applying ML/AI methods for autonomous systems from robotics through self-driving cars to organic and inorganic synthesis are generating enthusiasm for the potential of these techniques to enable automated and autonomous experiment (AE) in imaging. Here, we aim to analyze the major pathways towards AE in imaging methods with sequential image formation mechanisms, focusing on scanning probe microscopy (SPM) and (scanning) transmission electron microscopy ((S)TEM). We argue that automated experiments should necessarily be discussed in a broader context of the general domain knowledge that both informs the experiment and is increased as the result of the experiment. As such, this analysis should explore the human and ML/AI roles prior to and during the experiment, and consider the latencies, biases, and knowledge priors of the decision-making process. Similarly, such discussion should include the limitations of the existing imaging systems, including intrinsic latencies, non-idealities and drifts comprising both correctable and stochastic components. We further pose that the role of the AE in microscopy is not the exclusion of human operators (as is the case for autonomous driving), but rather automation of routine operations such as microscope tuning, etc., prior to the experiment, and conversion of low latency decision making processes on the time scale spanning from image acquisition to human-level high-order experiment planning. Overall, we argue that ML/AI can dramatically alter the (S)TEM and SPM fields; however, this process is likely to be highly nontrivial, be initiated by combined human-ML workflows, and will bring new challenges both from the microscope and ML/AI sides. At the same time, these methods will enable fundamentally new opportunities and paradigms for scientific discovery and nanostructure fabrication.