We study what kinds of limits are preserved by the greatest semilattice image functor from the category of all semigroups to its subcategory of all semilattices. The second author's research for this article was supported in part by Central European University ("CEU") Special and Extension Programs and by Estonian Science Foundation grant no. 6238. The third author's research was partially supported by Hungarian National Foundation for Scientific Research grant no. T43034. The second and the third authors thank the Estonian and the Hungarian Academies of Sciences for making possible mutual visits through their exchange agreement. 1