As of 2018 the message that urgent measures must be implemented to avoid planetary collapse owes much to the youth climate movement, led by, among others, activist Greta Thunberg. The main aim of this research is to explore the level of penetration of the urgency discourse, necessary to determine future communication strategies. Our methodological proposal is to measure the presence of the terms "climate crisis" and "climate emergency," in the Twitter conversation, as indicative of the degree of penetration of the discourse on urgency, as opposed to the term "climate change," which we associate to a discourse prevalent before the events of 2018, as well as to assess Thunberg's influence on the dissemination of said terms in the (digital) public sphere. The period under discussion covers 36 days, including the 2019 United Nations Climate Change Conference held in Madrid (Spain), from which we collected tweets (n=3,324,580) and analyzed the volume of the terms "climate change," "climate crisis," and "climate emergency." We conclude that discourse on the climate urgency is relevant on Twitter and that Thunberg could have played a major role in the increasing use of "climate crisis" over "climate change," though not so for "climate emergency."