بسم الله الرحمن الرحيم
First commentary
The first person known to write a commentary on Ṣaḥīḥ Al-Bukhārī is ʿAllāmah Khaṭṭābī (319-388 AH) (raḥimahullāh). His commentary is titled: أعلام الحديث في شرح صحيح البخاري which has been printed and is available.
Dr. Muḥammad ibn Saʿd Āl Saʿūd has done a taḥqīq on it and it has been published in four volumes by at-Turāth al-Islāmī. It is also published with the title Aʿlām al-Sunan fī Sharḥ Ṣaḥīḥ al-Bukhārī by DKI in two volumes. ʿAllāmah Khaṭṭābī (raḥimahullāh) discusses the correct spelling and vowelisation of the words of ḥadīth in length and brings many proofs for them from the Arabic language. He depended on the transmission of Imām Nasafī from the beginning of the book until the beginning of Kitāb at-Tafsīr, and then on the transmission of Imām Firabrī until Kitāb al- Fitan. He has commented only on some chapters of the Ṣaḥīḥ, and in those chapters, he has omitted some aḥadīth and kept only those that mention ambiguities that require clarification. Overall, his commentary is a lughawī (lexical) commentary. Lastly, there is a link between this commentary of his, and another one titled Maʿālim as-Sunan, as Imām Khaṭṭābī (raḥimahullāh) considers this commentary of his to complete the other.
Second commentary
The second person was Abū Jaʿfar Aḥmad al-Asadī Ad-Dawudi (raḥimahullāh) (d. 402 AH). We say he is the second person based on his date of demise, because we are unaware of when he was born and at which stage of his life he wrote his commentary. It could be possible that he was first assuming that he wrote his commentary in his youth whilst ʿAllāmah Khaṭṭābī wrote his in the final stages of his life. The name of his commentary is النصيحة في شرح البخاري but unfortunately, it is mafqūd (lost) and no manuscript is known today although many scholars of the past did have a copy.
Third commentary
The third known person is Imām Abū Bakr Ibn al-ʿArabī (468-543 AH) (raḥimahullāh). He wrote a commentary titled النيرين في شرح الصحيحين. As evident, it was not just a commentary of Ṣaḥīḥ al-Bukhārī but of both Al-Bukhārī and Muslim (ṣaḥīḥayn). This has not been published.
Imām Dhahabī (raḥimahullāh) in his Siyar Aʿlām an-Nubalāʾ (20:197) described Imām Ibn al-ʿArabī as “Al-Imām Al-ʿAllāmah Al-Ḥāfiẓ Al-Qāḍī”, and said that he had so much knowledge that some would say that he reached the status of individual ijtihād (i.e. mujtahid mutlaq) although he was a staunch Mālikī.
The Hadith Disciple 