Hydrogen exhibits the highest heating value per mass of all chemical fuels. Furthermore, hydrogen is regenerative and environmentally friendly. There are two reasons why hydrogen is not the major fuel of today's energy consumption. First of all, hydrogen is just an energy carrier. And, although it is the most abundant element in the universe, it has to be produced, since on earth it only occurs in the form of water and hydrocarbons. This implies that we have to pay for the energy, which results in a difficult economic dilemma because ever since the industrial revolution we have become used to consuming energy for free. The second difficulty with hydrogen as an energy carrier is its low critical temperature of 33 K (i.e. hydrogen is a gas at ambient temperature). For mobile and in many cases also for stationary applications the volumetric and gravimetric density of hydrogen in a storage material is crucial. Hydrogen can be stored using six different methods and phenomena: (1) high-pressure gas cylinders (up to 800 bar), (2) liquid hydrogen in cryogenic tanks (at 21 K), (3) adsorbed hydrogen on materials with a large specific surface area (at T<100 K), (4) absorbed on interstitial sites in a host metal (at ambient pressure and temperature), (5) chemically bonded in covalent and ionic compounds (at ambient pressure), or (6) through oxidation of reactive metals, e.g. Li, Na, Mg, Al, Zn with water. The most common storage systems are high-pressure gas cylinders with a maximum pressure of 20 MPa (200 bar). New lightweight composite cylinders have been developed which are able to withstand pressures up to 80 MPa (800 bar) and therefore the hydrogen gas can reach a volumetric density of 36 kg.m-3, approximately half as much as in its liquid state. Liquid hydrogen is stored in cryogenic tanks at 21.2 K and ambient pressure. Due to the low critical temperature of hydrogen (33 K), liquid hydrogen can only be stored in open systems. The volumetric density of liquid hydrogen is 70.8 kg.m-3, and large volumes, where the thermal losses are small, can cause hydrogen to reach a system mass ratio close to one. The highest volumetric densities of hydrogen are found in metal hydrides. Many metals and alloys are capable of reversibly absorbing large amounts of hydrogen. Charging can be done using molecular hydrogen gas or hydrogen atoms from an electrolyte. The group one, two and three light metals (e.g. Li, Mg, B, Al) can combine with hydrogen to form a large variety of metal-hydrogen complexes. These are especially interesting because of their light weight and because of the number of hydrogen atoms per metal atom, which is two in many cases. Hydrogen can also be stored indirectly in reactive metals such as Li, Na, Al or Zn. These metals easily react with water to the corresponding hydroxide and liberate the hydrogen from the water. Since water is the product of the combustion of hydrogen with either oxygen or air, it can be recycled in a closed loop and react with the metal. Finally, the metal hydroxides can be thermally reduced to metals in a solar furnace. This paper reviews the various storage methods for hydrogen and highlights their potential for improvement and their physical limitations.