This paper reviews a class of methods to perform causal inference in the framework of a structural vector autoregressive model. We consider three different settings. In the first setting, the underlying system is linear with normal disturbances and the structural model is identified by exploiting the information incorporated in the partial correlations of the estimated ressiduals. Zero partial correlations are used as input of a search algorithm formalized via graphical causal models. In the second, semi-parametric setting the underlying system is linear with nongaussian disturbances. In this case, the structural vector autoregressive model is identified through a search procedure based on independent component analysis. Finally, we explore the possibility of causal search in a nonparametric setting by studying the performance of conditional independence tests based on kernel density estimations.