  This paper is devoted to explore modified $f(\mathcal{R})$ theories of
gravity using Noether symmetry approach. For this purpose,
Friedmann-Robertson-Walker spacetime is chosen to investigate the cosmic
evolution. The study is mainly divided into two parts: Firstly Noether
symmetries of metric $f(\mathcal{R})$ gravity are revisited and some new class
of solutions with the help of conserved quantities are reported. It is shown
that different scenarios of cosmic evolution can be discussed using Noether
symmetries and one of the case indicates the chances for the existence of Big
Rip singularity. Secondly, $f(\mathcal{R})$ theory coupled with scalar field
has been discussed in detail. The Noether equations of modified gravity are
reported with three subcases for flat Friedmann-Robertson-Walker universe. It
is concluded that conserved quantities are quite helpful to find some important
exact solutions in the cosmological contexts. Moreover, the scalar field
involved in the modified gravity plays a vital role in the cosmic evolution and
an accelerated expansion phase can be observed for some suitable choices of
$f(\mathcal{R},\varphi,\chi)$ gravity models.
