The spectral analysis of regularly-sampled (RS) data is a well-established topic, and many useful methods are available for performing it under different sets of conditions. The same cannot be said about the spectral analysis of irregularly-sampled (IS) data: despite a plethora of published works on this topic, the choice of a spectral analysis method for IS data is essentially limited, on either technical or computational grounds, to the periodogram and its variations. In our opinion this situation is far from satisfactory, given the importance of the spectral analysis of IS data for a considerable number of applications in such diverse fields as engineering, biomedicine, economics, astronomy, seismology, and physics, to name a few. In this paper we introduce a number of IS data approaches that parallel the methods most commonly used for spectral analysis of RS data: the periodogram (PER), the Capon method (CAP), the multiple-signal characterization method (MUSIC), and the estimation of signal parameters via rotational invariance technique (ESPRIT). The proposed IS methods are as simple as their RS counterparts, both conceptually and computationally. In particular, the fast algorithms derived for the implementation of the RS data methods can be used mutatis mutandis to implement the proposed parallel IS methods. Moreover, the expected performance-based ranking of the IS methods is the same as that of the parallel RS methods: all of them perform similarly on data consisting of well-separated sinusoids in noise, MUSIC and ESPRIT outperform the other methods in the case of closely-spaced sinusoids in white noise, and CAP outperforms PER for data whose spectrum has a small-to-medium dynamic range (MUSIC and ESPRIT should not be used in the latter case).