Hydrogen is increasingly seen as a key energy carrier in transitioning towards a decarbonized global energy system. When considering the transportation sector, aviation stands out as one of the most hard-to-abate activities. Aviation is responsible for emitting 2.5% of the global CO2 from fossil sources before 2020, and it has been increasing at a rate of 4-5% per year since 2010. Hydrogen as a sustainable fuel for propulsion is recognized as a potential solution to meet the emission goals, however, several technical hurdles must be addressed when designing the storage system. This paper focuses on storing hydrogen in its liquid form within short- and medium-haul commercial aircraft. Different technological options are presented, covering the possible solutions described in the open literature. The main challenge of integrating a liquid hydrogen tank into the airframe is associated with its low volumetric density when compared to conventional jet fuels. In fact, the large volumes occupied by the liquid hydrogen tanks can be detrimental to the aerodynamics of the aircraft. This paper indicates that a universal solution does not exist yet. The decision on the tank-fuselage integration is arbitrary and depends on the scope of the work: non-integral tanks provide shape flexibility, and integral tanks provide volumetric efficiency. Aluminum alloy 2219, and closed-cell foams are leading the field when assessing the selection of the tank materials. Promising alternatives to enable lighter and safer solutions, such as composite materials and internal insulation systems, still require further studies in the cryogenic region of operation.