The paper presents a theory of excitonic polarons, which are quasiparticles formed by the interaction between an exciton and the surrounding lattice, leading to their localization. The theory is designed to be amenable to first-principles calculations and is applied to model Hamiltonians and real materials. Key findings include: 1. **Model Hamiltonians**: The theory is applied to Wannier excitons with Fröhlich or Holstein electron-phonon couplings. For Fröhlich interactions, excitonic polarons form only when there is a significant difference between electron and hole effective masses. 2. **Lithium Fluoride (LiF)**: The theory is used to calculate excitonic polarons in LiF, demonstrating its applicability to a variety of materials. The method does not require supercells, making it computationally efficient. 3. **Theoretical Formulation**: The total energy of the excitonic polaron is derived, and the theory is expressed in terms of the BSE Hamiltonian and exciton-phonon coupling matrix elements. Two alternative formulations are presented: the transition basis approach and the exciton basis approach. 4. **Qualitative Analysis**: The theory is applied to the Wannier exciton model with Fröhlich and Holstein electron-phonon interactions to gain insights into the formation of excitonic polarons. The total energy is evaluated in both the transition basis and exciton basis approaches, providing a qualitative understanding of the mechanisms involved. 5. **Computational Efficiency**: The exciton basis approach significantly reduces computational costs compared to the transition basis approach, making it suitable for large-scale calculations. 6. **Connection to Previous Work**: The theory connects to previously developed ab initio polaron equations and provides a formal connection to the Landau-Pekar model of polarons. Overall, the paper provides a comprehensive framework for understanding and calculating excitonic polarons in real materials using first-principles methods.The paper presents a theory of excitonic polarons, which are quasiparticles formed by the interaction between an exciton and the surrounding lattice, leading to their localization. The theory is designed to be amenable to first-principles calculations and is applied to model Hamiltonians and real materials. Key findings include: 1. **Model Hamiltonians**: The theory is applied to Wannier excitons with Fröhlich or Holstein electron-phonon couplings. For Fröhlich interactions, excitonic polarons form only when there is a significant difference between electron and hole effective masses. 2. **Lithium Fluoride (LiF)**: The theory is used to calculate excitonic polarons in LiF, demonstrating its applicability to a variety of materials. The method does not require supercells, making it computationally efficient. 3. **Theoretical Formulation**: The total energy of the excitonic polaron is derived, and the theory is expressed in terms of the BSE Hamiltonian and exciton-phonon coupling matrix elements. Two alternative formulations are presented: the transition basis approach and the exciton basis approach. 4. **Qualitative Analysis**: The theory is applied to the Wannier exciton model with Fröhlich and Holstein electron-phonon interactions to gain insights into the formation of excitonic polarons. The total energy is evaluated in both the transition basis and exciton basis approaches, providing a qualitative understanding of the mechanisms involved. 5. **Computational Efficiency**: The exciton basis approach significantly reduces computational costs compared to the transition basis approach, making it suitable for large-scale calculations. 6. **Connection to Previous Work**: The theory connects to previously developed ab initio polaron equations and provides a formal connection to the Landau-Pekar model of polarons. Overall, the paper provides a comprehensive framework for understanding and calculating excitonic polarons in real materials using first-principles methods.