With the advancement of technology, there is an increase in scale and scope of datasets exhibiting non-trivial characteristics such as skewness, varying tailweight or multimodality. However, the classical circular distributions are mostly symmetric and unimodal and cannot model this type of data accurately. Due to the increasing demand for new flexible distributions able to capture these features, different distributions have been proposed in recent years by applying the weighting approach on the existing circular distributions but it comes as a surprise that no paper addresses the weighting approach on the circle from a general viewpoint. On the real line this approach is one of the most common ways to build new models. In this chapter we therefore present a general study of the weighting approach on the circle.