Mobile applications are increasingly being built using web technologies as a common substrate to achieve portability and to improve developer productivity. Unfortunately, web applications often incur large performance overhead, directly affecting the user quality-of-service (QoS) experience. Traditional techniques in improving mobile processor performance have mostly been adopting desktop-like design techniques such as increasing single-core microarchitecture complexity and aggressively integrating more cores. However, such a desktop-oriented strategy is likely coming to an end due to the stringent energy and thermal constraints that mobile devices impose. Therefore, we must pivot away from traditional mobile processor design techniques in order to provide sustainable performance improvement while maintaining energy efficiency. In this article, we propose to combine hardware customization and specialization techniques to improve the performance and energy efficiency of mobile web applications. We first perform design-space exploration (DSE) and identify opportunities in customizing existing general-purpose mobile processors, that is, tuning microarchitecture parameters. The thorough DSE also lets us discover sources of energy inefficiency in customized general-purpose architectures. To mitigate these inefficiencies, we propose, synthesize, and evaluate two new domain-specific specializations, called the Style Resolution Unit and the Browser Engine Cache. Our optimizations boost performance and energy efficiency at the same time while maintaining generalpurpose programmability. As emerging mobile workloads increasingly rely more on web technologies, the type of optimizations we propose will become important in the future and are likely to have a long-lasting and widespread impact.