Abstract: The classical conjecture of M. Kneser and J. Tits asserts that if $G$ is an algebraic group defined over $k$ and is isotropic over $k$ (for example $G=SO(Q)$ for a quadratic form that has nontrivial zeros over $k$, or $G=SL(n), SP(2n)$ etc.) then the abstract group $G(k)$ is generated by certain unipotent elements (in the above examples, this just means matrices with all eigenvalues equal to $1$). This was shown to be true for local fields by V. Platonov and false in general. This conjecture for a certain form of $E_8$ has a reformulation in terms of groups of type $E_6$ and $F_4$ and has some interesting consequences. The conjecture of Tits and Weiss is for groups of type $E_6$. We will explain this conjecture in a least technical manner and report on some progress.