Some conjectures and results about multizeta values for F_q[t]

In this paper, we explain several conjectures about how a product of two Carlitz-Goss zeta values can be expressed as a F_p-linear combination of Thakur's multizeta values, generalizing the q=2 case dealt by D. Thakur in Relations between multizeta values for F_q[t]. In contrast to the classical sum shuffle, \zeta(a)\zeta(b)=\zeta(a+b)+\zeta(a,b)+\zeta(b,a), the identities we get are much more involved. Hundreds of instances of these conjectures have been proved and we describe the proof method and the evidence.