We present basic properties of the Fourier and the Fourier–Stieltjes algebras of locally compact groups and discuss the results of Cohen, Ilie-Spronk and Daws on homomorphisms of Fourier algebras. We provide necessary and sufficient conditions for the existence of idempotents of arbitrarily large norms in the Fourier-Stieltjes algebra B(G) of a locally compact group G. We prove that B(G) contains idempotents of arbitrarily large norm if and only if there are homomorphisms of arbitrarily large norm from the Fourier algebra A(H) into B(G) for any locally compact group H. The results are from joint work with Eleftherakis and Katavolos (Stud. Math. 267:109–120, 2022, [1]).