The f-block of the periodic table of the elements consists of those elements (sometimes referred to as the inner transition elements) for which, in the atomic ground state, the highest-energy electrons occupy f-orbitals.
Unlike the other blocks, the conventional divisions of the f-block follow periods of similar atomic number rather than groups of similar electron configuration. Thus, the f-block is divided into the lanthanoid series and the actinoid series.  
The name 'inner transition' is derived by analogy with the transition metals.
Like the s-block, the elements of the f-block are highly reactive metals. They catch fire in air very easily, and react with water to liberate hydrogen. Physically they are denser and have higher melting and boiling points than the alkaline earth metals, but their reactivity makes them of very limited use structurally. They are used together to make cigarette lighter flints because they catch fire in air so easily. Most of them are extracted by electrolysis of molten chlorides: the metals are much too reactive to be extractable from aqueous solutions.
The compounds of most f-block elements are ionic salts with M3+ ions, often hydrated in aqueous solutions. Cerium also forms a small series of strongly oxidising compounds with the +4 oxidation state, including ceric oxide (CeO2). The lighter actinides (protactinium to americium) have f-electrons that can participate in bonding and form compounds in a variety of oxidation states from +2 to +6. Owing to the pulling of the inner f-electrons towards the nucleus, the heavier actinides (curium to lawrencium) tend not to use their inner f-electrons and resemble the lanthanides in forming salts with M3+ ions.
Interactive f-orbital models can be found at this site: