Post-quantum cryptography is an active field of research in developing new cryptosystems that willbe resistant to attack by future quantum computers. Recently a somewhat obscure area, isogeny-based cryptography, has been getting more attention,including impressive speed and compression optimizations and robust security analyses, bringing it into regular discussion alongside other post-quantum candidates. This talk will cover isogeny-based crypto, specifically these recents results regarding supersingular isogeny diffie-hellman, whichis a possible replacement for the ephemeral key exchanges in use today.