The relation between surface structure and reactivity of oxygen on Rh(110) has been studied by means of AES, LEED and TPD. Various oxygen surface structures are produced by changing the oxygen coverage, theta(O), and surface temperature. At temperatures below 300 K and oxygen coverages larger than 0.4 only a (2 x 1)p2mg LEED pattern was observed. Heating to 470 K leads to a c(2 x 8) pattern at nearly monolayer coverage and to c(2 x 2n) structures at 0.6 < theta(O) < 1. At half monolayer coverage a (2 x 2)p2mg structure is formed after heating above 470 K. The reactivity of oxygen in the different surface structures towards CO and H-2 has been investigated and found to be higher for the (2 x 2)p2mg than for the c(2 x 2n) structure. After reduction of the (2 x 2)p2mg and c(2 x 2n) oxygen structures, metastable (1 x n) structures are produced which revert to (1 x 1) at temperatures above 470 K. Models for some of the oxygen structures are suggested on the basis of the LEED data and the observed differences in the reactivity of oxygen.