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We extend results of Gy\'arf\'as and F\"uredi on the largest monochromaticcomponent in $r$-colored complete $k$-uniform hypergraphs to the setting ofrandom hypergraphs. We also study long monochromatic loose cycles in$r$-colored random hypergraphs. In particular, we obtain a random analog of aresult of Gy\'arf\'as, S\'ark\"ozy, and Szemer\'edi on the longestmonochromatic loose cycle in $2$-colored complete $k$-uniform hypergraphs.

Large monochromatic components and long monochromatic cycles in random hypergraphs