This is an announcement for the paper “Interpolation and extrapolation of strictly singular operators between $L_p$ spaces” by Francisco L. Hernández<https://arxiv.org/find/math/1/au:+Hernandez_F/0/1/0/all/0/1>, Evgeny M. Semenov<https://arxiv.org/find/math/1/au:+Semenov_E/0/1/0/all/0/1>, Pedro Tradacete<https://arxiv.org/find/math/1/au:+Tradacete_P/0/1/0/all/0/1>. Abstract: We study the interpolation and extrapolation properties of strictly singular operators between different $L_p$ spaces. To this end, the structure of strictly singular non-compact operators between $L_p-L_q$ spaces is analyzed. Among other things, we clarify the relation between strict singularity and the $L$-characteristic set of an operator. In particular, Krasnoselskii's interpolation theorem for compact operators is extended to the class of strictly singular operators. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1706.08682