We study the external and internal Zappa-Szep product of topological groupoids. We show that under natural continuity assumptions the Zappa-Szep product groupoid is etale if and only if the individual groupoids are etale. In our main result we show that the C*-algebra of a locally compact Hausdorff etale Zappa-Szep product groupoid is a C*-blend, in the sense of Exel, of the individual groupoid C*-algebras. We finish with some examples, including groupoids built from *-commuting endomorphisms, and skew product groupoids.
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