It is well known that Shor's algorithm can solve the integer factorization problem and the discrete logarithm problem in polynomial time, which makes classical cryptosystems insecure. Hence, more and more post-quantum cryptosystems emerge at present such as lattice-based, code-based, hash-based, and isogeny-based cryptosystems. Compared with other cryptosystems, the isogeny-based cryptosystems have the advantages of short key size. Nevertheless, it does not outperform other cryptosystems in respect of implementation efficiency. Based on two types of key exchange protocols from supersingular elliptic curve isogeny, this paper analyzes the possibility of optimizing two key exchange protocols according to the classical optimizations of elliptic curve scalar multiplication and pairing as well as some characteristics of elliptic curve isogeny. Meanwhile, the paper categorizes and reviews the current progress on efficient isogenous computations, and puts forward the further researches in this direction.