In short, airplanes happened. First lighter-than-air, mechanically propelled aircrafts were designed long before heavy flying machines were demonstrated to be a viable concept, but much like electric cars that predated the ones using combustion engines, dirigibles quickly reached the technical constraints that made the upgrades and development very hard, ultimately causing such vehicles to be considered a dead end.

The first dirigible balloon has been flown in 1852, when the balloon equipped with steam engine and designed by Henri Jules Giffard successfully flew the Paris-Élancourt route, maintaining an average speed of 6 mph (9 km/h). Three decades later, in 1884, the first electrically-powered airship christened 'La France' has been flown and although it traveled only slightly over 4 miles (7.5 km), it demonstrated the speed of 13 mph (20 km/h). The first rigid airship was envisioned by Ferdinand count von Zeppelin and designed by Theodor Kober, having been subsequently built and flown in 1900. This vehicle was simply called 'Luftschiff Zeppelin' (Zeppelin Airship) which name apparently stuck after quick development and popularization of the concept in Germany and abroad.

The main problem of the airships was the fact that they were essentially lighter-than air devices, and thus were utilizing the principle of buoyancy that put a severe limitation on the potential development. To make the dirigible buoyant, its general density must have been lower than that of air (what also limits the practical ceiling as the density of atmosphere lowers with the increase of altitude) what can be achieved either by filling the gas cells (essentially balloons held within the frame of the rigid airships or attached to the canopy of the non-rigid and semi-rigid ones) with a low-density gas or evacuating them so that they basically contain nothing. The latter solution was considered nigh-impossible (although metal-body airships were built as a proof of concept), as there was no material that could have both keep a shape after being subjected to the 1 atm difference of pressures and be light enough to provide buoyancy, so the only practical way was to use lighter-than-air gases.

The obvious choice was the lightest and very abundant element i.e. hydrogen, with the inert helium being close second choice. But both have significant drawbacks. Hydrogen is very abundant, easy to manufacture but also very flammable and even explosive when mixed with oxygen with an additional problem of keeping it stored due to extreme volatility. Conversely, helium is very safe and though it is one of the most abundant elements in the universe, it is quite rare on Earth and thus the increased demand could have easily ramped up the price, making the airship operation progressively more expensive.

Given that the density of air is on average 1.165 (at 500 m asl) with the corresponding value equal to 0.176 g/l for helium and 0.089 g/l for hydrogen, it means, using rough approximation, that one cubic meter of hydrogen could potentially have lifted up to 1 kg of mass to an altitude of 500 m, including the mass of the gas container itself. This seems quite a lot, given the size of the airships, but between the large dural frame and the gas cells or the outer cover made of several layers of cotton cloth reinforced with rubber compounds, the empty weight of the zeppelins was substantial. Largest airships of the 1930s, such as LZ 127 Hindenburg or USS Akron had a displacement of 200.000 cubic meters, what with the nominal filling rate of 92-95% and their mass approaching roughly 110-115 metric tons usually left 75-80 tons of lift available for cargo, supplies, crew, armament, fuel, airplanes etc.

The airships proved to be a competition for the ocean liners as far as the transatlantic passenger transport was concerned. Until the late 1930s, land-based airplanes (i.e. not the seaplanes) were still not capable of such a feat, making airships the only means of transcontinental air travel. But between the lull in transatlantic tourism in early 1940s for the obvious reasons and the rapid development of airplanes up to and including the first jet engines, it became more and more obvious that the airships are largely a dead end. The same applied to the shorter routes, that were much more conveniently accommodated by the airplanes that were often cheaper to manufacture and did not require complex infrastructure due to far smaller size (and thus far smaller hangars) and simple landings that did not necessitated large mooring crews and complex procedures. Additionally, further technological developments allowed the airplanes to achieve far higher speeds, dramatically shortening the duration of travel. In 1937, LZ 129 Hindenburg, one of the most modern passenger airships was able to cover the route of Frankfurt-Lakehurst (3900 mi or 6280 km) in averagely 65 hours flying westward and 53 hours on the route eastward. Less than a decade later, Lockheed L-049 plane carrying the number of passengers similar to the capacity of the biggest airships was consistently covering New York-London route (3420 mi or 5511 km) in slightly over 15 hours, less than the difference between the upper and lower travel time of the aforementioned LZ 129 Hindenburg, achieving average travel speed of 225 mph (360 km/h). Less than two years later, in 1948, the first jet airliner, Vickers VC.1 equipped with Rolls-Royce RB.41 turbojet engines during a test London-Paris flight achieved the average speed of 395 mph (634 km/h).

It also should be noted that the 'Hindenburg' crash did not need to be of that great importance here, as the German usage of hydrogen as the lift gas has been largely caused by necessity, as their relations with USA became strained and the latter were the only manufacturer of helium in the world, meaning that the Lakehurst catastrophe was of little importance to American airship industry that largely used helium as the lift gas. Of course, the Herbert Morrison commentary to the film material showing the demise of the 'Hindenburg' could have strongly eroded trust in this mode of transportation in USA, but this might not necessarily translate well to the public image of airship in other countries. After all, Germans continued to construct subsequent liner airships, most notably LZ 130 and LZ 131, with the former being finished and used for military reconnaissance during flights tests in 1938 and 1939. On the other hand, with the liner airships being relatively few and the prices of the voyage being quite high (comparable with modern first-class flights on similar routes), even small-scale reluctance could have been a death knell for the entire industry.

Interestingly, the airships themselves were never considered obsolete, and they were produced by various companies, mainly in Germany, Great Britain and USA (German Luftschiffbau Zeppelin GmbH still exists). Thanks to the new technological developments, mainly in the field of the modern plastics and miniaturization of engines, airships saw a limited resurrection in early 1970s and later in mid-1995, with the new vehicles, thanks to low costs of operation, safety of operation and the ability to maintain slow speeds are used as the civilian advertisement carriers, novelty tourist transport and patrol vehicles for various services, from maritime traffic monitoring to border patrol.

EDIT: Corrected several typos and spelling errors.