Automatic text summarization systems commonly involve humans for preparing data or evaluating model performance, yet, there lacks a systematic understanding of humans' roles, experience, and needs when interacting with or being assisted by AI. From a human-centered perspective, we map the design opportunities and considerations for human-AI interaction in text summarization and broader text generation tasks. We first conducted a systematic literature review of 70 papers, developing a taxonomy of five interactions in AI-assisted text generation and relevant design dimensions. We designed text summarization prototypes for each interaction. We then interviewed 16 users, aided by the prototypes, to understand their expectations, experience, and needs regarding efficiency, control, and trust with AI in text summarization and propose design considerations accordingly.