My PhD thesis studied the asymptotic behavior of the number of zeros of random trigonometric functions on a fixed interval — almost surely, in distribution, and on average — with a particular focus on universality: to what extent this behavior depends on the law of the coefficients, their correlations, or the choice of basis functions. Working with dependent stationary Gaussian processes, dependence is encoded through the associated spectral measure, whose nature has a decisive impact on the asymptotics and produces both universal and genuinely non-universal regimes. The analysis combines the Kac–Rice formula with techniques inspired by classical work of Salem and Zygmund, and yields new global universality and non-universality results for the zero sets of random trigonometric polynomials.