Highlighting a number of perspectives from critical social theory and research as well as critical language and discourse studies, this paper explores conceptions of normalisation particularly relevant to the analysis of its dynamics and trajectories in public discourse. Starting by disentangling the complex relationship between norms, normality, normalization and discourse, the article argues that two major trends in research on normalization of violence and deviancehave been particularly influential in designing theories and analyses of normalisation processes. They have also been pivotal in pointing to path-dependencies of normalization processes, to the centrality of classification, distinction and stigmatization or to the role of pre-/legitimation and legitimation via social imaginaries as those which characterise the introduction and communication of new norms and normativites in the public domain. Crucially, many of those features of normalization are often both sustained and nested in context-dependent formats of normalization discourse. The latter, drawing on a wide array of discursive and linguistic features explored in the article, effectively enables the orchestration of new discursive shifts in public discourse as well as the introduction and pre-/legitimation of new or recontextualised norms and perceptions of what is, and what is not, acceptable and unacceptable in politics, media, institutions and beyond.