Marine bugs of the genus Halovelia Bergroth inhabit intertidal coral reefs and rocky coasts along the continents and larger islands bordering the Red Sea, Indian Ocean, and western Pacific Ocean as well as on island groups and atolls in these areas. A historical review of the study of the genus is presented and different views upon its classification discussed. The genus Halovelia is redescribed together with its type species, H. maritima Bergroth, and four other previously known species. Fifteen new species are described: H. carolinensis sp.n. (Caroline Islands), H. halophila sp.n. (Sumbawa, Sabah), H. corallia sp.n. (Papua New Guinea, Australia: Queensland), H. esakii sp.n. (Solomon Islands, Irian New Guinea, Moluccas, Sulawesi, Sumbawa, Palau Islands, Philippines), H. polhemi sp.n. (Australia: Northern Territory), H. solomon sp.n. (Solomon Islands), H. novoguinensis sp.n. (Papua New Guinea), H. fosteri sp.n. (Fiji Islands), H. tongaensis sp.n. (Tonga Islands), H. heron sp.n. (Australia: S. Queensland), H. fijiensis sp.n. (Fiji Islands), H. inflexa sp.n. (Sudan, Red Sea), H. annemariae sp.n. (Solomon Islands, Papua New Guinea), H. lannae sp.n. (Java, Singapore, West Malaysia, Sabah, Philippines), and H. wallacei sp.n. (Sulawesi, Sumbawa). Two names are synonymized: H. marianarum Usinger syn.n. (= H. bergrothi Esaki) and H. danae Herring syn.n. (= H. bergrothi Esaki). The following species are removed from the genus Halovelia: H. papuensis Esaki, H. loyaltiensis China, and H. (Colpovelia) angulana Polhemus. A key to the species is included. The taxonomy of the H. malaya-group will be presented in Part II of this work together with the cladistics, ecology, biology, and biogeography of the genus.