The late 19th century saw deliberate research on the deep oceans, including depth sounding, and collecting samples by dredging and netting. The pioneering study was the Challenger expedition (1872-1876), named after the research ship HMS Challenger, originally built as a stem-and-sail corvette, and launched in 1858. The expedition was organised by the Royal Society of London and the University of Edinburgh, with the Challenger provided by the government. As far as marine biology went, the Challenger expedition discovered about 4,700 new species, including many deep-sea species. Previously, it had been commonly believed that the ocean depths were lifeless, and one of the major scientific objectives of the expedition was to get a first look at life in the ocean depths and on deep ocean seafloors (thus, the deep ocean netting and dredging to sample life in the depths).
The technology used by the Challenger expedition remained than main deep-ocean exploration methods until the development of deep-diving submersibles (manned and unmanned) and sonar that could map the deep-ocean seafloor.
Some deep-ocean species were discovered before then, when specimens were caught in shallow water, or discovered in the stomachs of other animals. Notably, the humpback anglerfish (Melanocetus johnsonii), discovered in 1863, inhabits the mesopelagic zone, where some light still reaches, about 200-1000m deep, and has been found as shallow as 100m. The paper describing the new species doesn't mention the depth it was caught at. Similaerly, Krøyer's angler fish (Ceratias holboelli), discovered before M. johnsonii, usually lives at depths of 400-2000m, but has been found at very shallow depths. The gulper eel (Saccopharynx ampullaceus) was discovered in 1826, found floating on the surface (still alive, and trying to eat a fish) by a whaler. The long snouted lancetfish (Alepisaurus ferox), scientifically discovered in 1860, migrates vertically during the day, and can be found from shallow depths to as deep as about 2000m. Today, it is commonly caught as bycatch, e.g., in longline tuna fishing.
Thus, the early discoveries of deep-sea fishes were fishes that often came up into shallow waters, or isolated specimens that came into unusually shallow waters for the species. Since these were fish not usually seen in shallow waters, it was suspected by many that they lived in the deep oceans.
For some further details on the Challenger expedition and modern-day deep-sea exploration, see
including a picture of HMS Challenger's netting and dredging equipment.