Methane functionalization is the process of converting methane in its gaseous state to another molecule with a functional group, typically methanol or acetic acid, through the use of transition metal catalysts.
In the realm of carbon-hydrogen bond activation and functionalization (C-H activation/functionalization), many recent efforts have been made in order to catalytically functionalize  the C-H bonds in methane. The large abundance of methane in natural gas or shale gas deposits presents a large potential for its use as a feedstock in modern chemistry. However, given its gaseous natural state, it is quite difficult to transport economically. Its ideal use would be as a raw starting material for methanol or acetic acid synthesis, with plants built at the source to eliminate the issue of transportation. Methanol, in particular, would be of great use as a potential fuel source, and many efforts have been applied to researching the feasibilities of a methanol economy.
The challenges of C-H activation and functionalization present themselves when several factors are taken into consideration. Firstly, the C-H bond is extremely inert and non-polar, with a high bond dissociation energy, making methane a relatively unreactive starting material. Secondly, any products formed from methane would likely be more reactive than the starting product, which would be detrimental to the selectivity and yield of the reaction. 
The main strategy currently used to increase the reactivity of methane uses transition metal complexes to activate the carbon-hydrogen bonds. In a typical C-H activation mechanism, a transition metal catalyst coordinates to the C-H bond to cleave it, and convert it into a bond with a lower bond dissociation energy. By doing so, the product can be used in further downstream reactions, since it will usually have a new functional group attached to the carbon. It is also important to note the difference between the terms "activation" and "functionalization," since both terms are often used interchangeably, but should be held distinct from each other. Activation refers to the coordination of a metal center to the C-H bond, whereas functionalization occurs when the coordinated metal complex is further reacted with a group "X" to result in the functionalized product.