  Circulant graphs are an important class of interconnection networks in
parallel and distributed computing. Integral circulant graphs play an important
role in modeling quantum spin networks supporting the perfect state transfer as
well. The integral circulant graph $\ICG_n (D)$ has the vertex set $Z_n = \{0,
1, 2, ..., n - 1\}$ and vertices $a$ and $b$ are adjacent if $\gcd(a-b,n)\in
D$, where $D \subseteq \{d : d \mid n,\ 1\leq d<n\}$. These graphs are highly
symmetric, have integral spectra and some remarkable properties connecting
chemical graph theory and number theory. The energy of a graph was first
defined by Gutman, as the sum of the absolute values of the eigenvalues of the
adjacency matrix. Recently, there was a vast research for the pairs and
families of non-cospectral graphs having equal energies. Following [R. B.
Bapat, S. Pati, \textit{Energy of a graph is never an odd integer}, Bull.
Kerala Math. Assoc. 1 (2004) 129--132.], we characterize the energy of integral
circulant graph modulo 4. Furthermore, we establish some general closed form
expressions for the energy of integral circulant graphs and generalize some
results from [A. Ili\' c, \textit{The energy of unitary Cayley graphs}, Linear
Algebra Appl. 431 (2009), 1881--1889.]. We close the paper by proposing some
open problems and characterizing extremal graphs with minimal energy among
integral circulant graphs with $n$ vertices, provided $n$ is even.
