Due to the critical role of technical innovation in transitioning from fossil fuel energy to carbon-free alternatives, there is a widespread consensus among IAM teams regarding the necessity of modeling endogenous technical change (ETC). This paper systematically demonstrates current techniques and theoretical foundations for handling ETC in both demand-side and supply-side, using the E3METL model as an example. Modeling technological progress and innovation in IAMs is essential for understanding technology competition and evolution, leading to more reasonable and insightful results. However, IAMs still lack a systematic framework for the development of ETC, requiring sectoral innovation mechanisms to develop endogenous technology modules and support the economic and social changes of technological innovation. Meanwhile, emerging techniques such as the socio-technical approach, innovation diffusion, and agent-based interactions show promise for ETC when integrated with IAMs. Furthermore, it is important to recognize that ETC interacts more extensively with non-energy systems, such as land, biological systems, and human health, than commonly assumed. This underscores the need for assessments within a more realistic framework and redesigning in conjunction with international cooperation.