Given an oriented closed surface S of genus g≧2, we can define the so-called Teichmuller space denoted by T(S). This space, which classifies in some sense conformal (or hyperbolic) structures on S, can be viewed as an open ball of real dimension 6g − 6. Moreover, this space is endowed with a “canonical” metric (the Teichmuller metric) which is associated with an important conformal invariant, the extremal length. This invariant allows us to define a compactification of Teichmller space, called the Gardiner-Masur compactification. The study of such a compactification is now part of the so-called Extremal length geometry. In this talk, we shall start by giving an overview of works did by Prof. Miyachi. Then, we shall deal with the horocyclic deformation, a conformal analogue of the Fenchel-Nielsen deformation and we shall prove that in some cases these conformal deformations converge towards the Gardiner-Masur boundary. If time permits, we shall talk about reduced compactifications of Teichmuller space and explain how they are connected to each others. A large part of this talk is based on a joint work with Prof. Miyachi and Prof. Ohshika.