In this paper, we present a theoretical analysis of the limits of the differential fault analysis (DFA) of AES by developing an inter-relationship between conventional cryptanalysis of AES and DFAs. We show that the existing attacks have not reached these limits and present techniques to reach these. More specifically, we propose optimal DFA on states of AES-128 and AES-256. We also propose attacks on the key schedule of the three versions of AES, and demonstrate that these are some of the most efficient attacks on AES to date. Our attack on AES-128 key schedule is optimal, and the attacks on AES-192 and AES-256 key schedule are very close to optimal. Detailed experimental results have been provided for the developed attacks. The work has been compared to other works and also the optimal limits of DFA of AES.