This paper summarizes a talk given by the author at the Indian Academy of Sciences, Bengaluru on December 12, 2019. It outlines the multiplicity of situations where measurements on directions in two, three, or more dimensions are observed, and form the basis for answering various scientific questions. After briefly outlining the novelty in dealing with such data and the need for an entirely different set of analytical tools, one of the basic questions that arises before any further inference viz. testing isotropy of circular data, is addressed. The author was initiated into this topic of directional statistics by Professor C R Rao during the 1960s and is pertinent to this occasion celebrating him.