This chapter is an analysis of the frequency-power spectrum. It first discusses the probabilistic methods for detecting signatures of individual modes in the spectrum, including schemes that incorporate a Bayesian framework for the analysis. The chapter then turns to the automated detection of the ensemble signatures of the oscillations. Next, this chapter considers the detailed peak-bagging analysis, where a multiparameter model is fitted to the spectrum to provide robust estimates of parameters of the individual modes. It introduces the fundamentals, discusses the practical implementation and challenges, and finally considers the additional challenges posed by subgiants and red giants showing mixed modes.