As Dennard scaling broke down in the 2000s and Moore’s Law slowed down in the 2010s, computer engineers have been exploring new ways to extract more computing performance without increasing the power density or the transistor count. Various specialized hardware accelerators are integrated into existing multi-core architectures, creating heterogeneous system-on-chips (SoC). However, as more heterogeneous SoCs are built, the number of different hardware blocks in a single SoC is rapidly increasing. This trend significantly increases the non-recurring engineering (NRE) cost required to build new SoCs. Maximizing the reuse of hardware blocks across and inside SoC designs is one of the key ways to reduce the NRE cost. This requires both flexible parameterization of a single hardware design block and versatile composition of numerous different hardware design blocks. To enable and maximize such reuse of hardware blocks, productive hardware modeling methodologies play a critical role in the modern computer engineeringworkflow. This thesis takes an engineering research approach to explore productive and extensible hardware modeling, simulation, and verification methodologies. I identify four major challenges in state-of-the-art productive hardware modeling methodologies and formulate each challenge into a stand-alone research question. Then, I propose several techniques to address these research questions: (1) native in-memory intermediate representation (NIMIR), a novel modular framework architecture, to improve the flexibility and extensibility of hardware generation and simulation frameworks (HGSF); (2) unified modular ordering constraints (UMOC), a novel modeling technique coupled with scheduling algorithms, to unify cycle- and register-transfer-level modeling and achieve high model fidelity with little effort; (3) Mamba++, a series of HGSF-aware just-in-time compilation (JIT) techniques and JIT-aware HGSF design techniques, to close the simulation performance gap in HGSFs; and (4) PyH2, our vision and techniques for testing various hardware designs leveraging open-source software, to reduce testing/verification time for agile hardware design flows. Finally, in addition to addressing each individual research question, I created PyMTL3, a new hardware generation and simulation framework which incorporates the techniques proposed in this thesis. By implementing the techniques inside a real hardware modeling framework, the practicality of the proposed techniques is demonstrated. PyMTL3 has been used in courses at Cornell University, in various research projects, and in several advanced-node chip tape-outs.