Demand for image editing has been increasing as users' desire for expression is also increasing. However, for most users, image editing tools are not easy to use since the tools require certain expertise in photo effects and have complex interfaces. Hence, users might need someone to help edit their images, but having a personal dedicated human assistant for every user is impossible to scale. For that reason, an automated assistant system for image editing is desirable. Additionally, users want more image sources for diverse image editing works, and integrating an image search functionality into the editing tool is a potential remedy for this demand. Thus, we propose a dataset of an automated Conversational Agent for Image Search and Editing (CAISE). To our knowledge, this is the first dataset that provides conversational image search and editing annotations, where the agent holds a grounded conversation with users and helps them to search and edit images according to their requests. To build such a system, we first collect image search and editing conversations between pairs of annotators. The assistant-annotators are equipped with a customized image search and editing tool to address the requests from the user-annotators. The functions that the assistant-annotators conduct with the tool are recorded as executable commands, allowing the trained system to be useful for real-world application execution. We also introduce a generator-extractor baseline model for this task, which can adaptively select the source of the next token (i.e., from the vocabulary or from textual/visual contexts) for the executable command. This serves as a strong starting point while still leaving a large human-machine performance gap for useful future work. Data and code are available: https://github.com/hyounghk/CAISE.