Developing aerial robots that can both safely navigate and execute assigned mission without any human intervention - i.e., fully autonomous aerial mobility of passengers and goods - is the larger vision that guides the research, design, and development efforts in the aerial autonomy space. However, it is highly challenging to concurrently operationalize all types of aerial vehicles that are operating fully autonomously sharing the airspace. Full autonomy of the aerial transportation sector includes several aspects, such as design of the technology that powers the vehicles, operations of multi-agent fleets, and process of certification that meets stringent safety requirements of aviation sector. Thereby, Autonomous Advanced Aerial Mobility is still a vague term and its consequences for researchers and professionals are ambiguous. To address this gap, we present a comprehensive perspective on the emerging field of autonomous advanced aerial mobility, which involves the use of unmanned aerial vehicles (UAVs) and electric vertical takeoff and landing (eVTOL) aircraft for various applications, such as urban air mobility, package delivery, and surveillance. The article proposes a scalable and extensible autonomy framework consisting of four main blocks: sensing, perception, planning, and controls. Furthermore, the article discusses the challenges and opportunities in multi-agent fleet operations and management, as well as the testing, validation, and certification aspects of autonomous aerial systems. Finally, the article explores the potential of monolithic models for aerial autonomy and analyzes their advantages and limitations. The perspective aims to provide a holistic picture of the autonomous advanced aerial mobility field and its future directions.