Pairings were first introduced in cryptology by Menezes, Okamoto & Vanstone and Frey & Rueck for code-breaking purposes. Mitsunari, Sakai & Kasahara and Sakai, Oghishi & Kasahara seem to be the first to have discovered their constructive properties. Since the foundational work of Joux in 2000, an already large and ever increasing number of pairing-based protocols has been found. The software implementations of these successive algorithmic improvements being rather slow, the need for fine hardware implementations is strong. This is a critical issue to make pairings popular and of common use in cryptography and in particular in view of a successful industrial transfer. We will start this talk by a reminder on pairings, and then present recent works that address the problem of getting efficient hardware implementation of the eta and Tate pairings on elliptic curves in characteristic 2 and 3. This is a joint work with Jean-Luc Beuchat (Univ. Tsukuba, Japan), Jrmie Detrey (B-IT, Bonn), Eiji Okamoto (Univ. Tsukuba), Masaaki Shirase (Future Univ. Hakodate, Japan), Tsuyoshi Takagi (Fut. Univ. Hakodate).