This will be a very broad and gentle overview of field towers, which are infinite sequences of fields with many useful applications. For instance, in the number field case they are used to get good bounds on the [K:Q]th root of |Disc(K)| and to obtain very dense lattices. In the function field case they produce families of curves over finite fields with many points but small genus, useful for coding theory and financial applications. A group of us intend to give a series of talks on this theme, this being the first.