This paper is a survey of the author’s recent works on special values of zeta functions and Galois representations associated with various automorphic forms. Let \(F\) be an algebraic number field and let \(S\) be a space of automorphic forms with respect to \(\text{GL}_ 1\) or \(\text{GL}_ 2\). For each integral ideal \(\mathfrak a\) of \(F\), a Hecke operator \(T(\mathfrak a)\) is defined as an automorphism of \(S\). If \(S\) is a module over an algebra \(A\), then the Hecke algebra \(\mathcal H\) is generated by \(T(\mathfrak a)\) and is a subalgebra of \(A\)-linear automorphisms of \(S4\). Let \(\lambda: \mathcal H\to A\) be a homomorphism of \(A\)-algebras. We introduce the zeta-function, \[ L(s,\lambda):=\sum_{\mathfrak a}| \lambda (T(\mathfrak a))|^ 2\cdot {\mathcal N}_{F/\mathbb Q}(\mathfrak a)^{-s}, \] where \({\mathcal N}_{F/\mathbb Q}\) means the norm function. This is the main object to analyze. \(L(s,\lambda)\) has simple poles at several positive integer points. We can prove that the residues of the poles are expressed as a product of a unit element and a natural transcendental divisor. In some concrete cases, the author investigates the properties of special values of \(L(s,\lambda)\) and the Galois representations attached to automorphic forms.