Strongly compact cardinals and the continuum function

We study the general problem of behaviour continuum function in presence non-supercompact strongly compact cardinals. begin by showing that it is possible to force violations GCH at an arbitrary cardinal using only strong compactness as our initial assumption. This result due third author. then investigate realising Easton functions and above least measurable limit supercompact cardinals starting from assumption existence a By results Menas, assuming 2κ=κ+, κ provably ZFC which not κ+-supercompact. also consider generalisations earlier theorems more than one cardinal. conclude with some open questions.