A choreography in the n-body problem is a periodic solution in which all bodies follow the same curve, equally spaced in time. In this talk, we will discuss the proof of the existence of a family of periodic solutions that connects the relative equilibrium of Lagranges equilateral triangle configuration with the figure-eight choreography in the three-body problem with equal masses. A general overview will be presented of the methods employed along this journey, including topological degree theory, numerical analysis, and computer-assisted proofs. In particular, we will highlight their role in addressing the Marchal conjecture, which plays a central part in the rigorous understanding of these solutions.