Conditional dependence often provides an interpretable way of formalising the relatedness between variables. Moreover, it may indicate a type of causal link, so it is of great interest to detect conditional dependencies from data. Conditional independencies can be conveniently represented through undirected graphs, while their directed analogues can additionally be used to indicate causal relationships. We present the PC algorithm for causal structure learning, as well as several approaches for testing conditional independence, both under a Gaussianity assumption and in a more general nonparametric context.