For any p-adic Galois representation, one can attach an analytic object (the complex-valued L-function) and an algebraic object (the Bloch--Kato Selmer group), and the conjecture of Bloch and Kato describes a precise relation between these two objects. More generally, one can often formulate an "Iwasawa main conjecture" for this representation, which predicts a relation between a p-adic L-function and the inverse limit of Selmer groups in a p-adic Lie extension. In this thesis, we explore the connection between Euler systems and both of these conjectures. More precisely, in the first part of this thesis, we construct a split anticyclotomic Euler system for the Galois representation associated with a cuspidal automorphic representation of a unitary group of signature (1, 2n-1), where n is an odd integer. Combining this with the forthcoming work of Jetchev--Nekovář--Skinner, one can control the size of the Bloch--Kato Selmer group provided the bottom class of the Euler system is non-zero. In the second part of this thesis, we discuss applications of Euler systems to supersingular Iwasawa theory in the case of the convolution of two Coleman families. In particular, we obtain some partial results concerning the support of the associated Selmer sheaf and the vanishing locus of the three-variable p-adic L-function constructed by Urban. This crucially relies on the machinery of Selmer complexes as developed by Nekovář and Pottharst.