Specializing chips using hardware accelerators has become the prime means to alleviate the gap between the growing computational demands and the stagnating transistor budgets caused by the slowdown of CMOS scaling. Much of the benefits of chip specialization stems from optimizing a computational problem within a given chip's transistor budget. Unfortunately, the stagnation of the number of transistors available on a chip will limit the accelerator design optimization space, leading to diminishing specialization returns, ultimately hitting an accelerator wall. In this work, we tackle the question of what are the limits of future accelerators and chip specialization? We do this by characterizing how current accelerators depend on CMOS scaling, based on a physical modeling tool that we constructed using datasheets of thousands of chips. We identify key concepts used in chip specialization, and explore case studies to understand how specialization has progressed over time in different applications and chip platforms (e.g., GPUs, FPGAs, ASICs)1. Utilizing these insights, we build a model which projects forward to see what future gains can and cannot be enabled from chip specialization. A quantitative analysis of specialization returns and technological boundaries is critical to help researchers understand the limits of accelerators and develop methods to surmount them.