Finite fields have for a long time been important in Applied Algebra, in particular in the theory of error correcting codes. In more recent times, they have assumed an equally important role in Cryptography, initially mainly in the generation of pseudorandom sequences and the design of stream ciphers, as we have seen. But more recently, especially since the selection of Rijndael in 2000/2001 as the Advanced Encryption Standard (AES), they have assumed a vitally important role in the design of block ciphers as well. In this chapter we discuss some aspects of these further applications.