Modified gravity theories are reviewed in the context of inflation, dark energy, and bouncing cosmology. The paper discusses various modified gravity frameworks, including $ F(R) $, $ F(\mathcal{G}) $, and $ F(T) $ gravity, as well as alternative theories. These theories are analyzed for their viability in describing the early universe's inflationary era, the late-time dark energy era, and bouncing cosmologies. The paper emphasizes the formalism of these theories and their ability to produce a viable inflationary era consistent with observational data. It also explores how bouncing cosmologies can be described within these frameworks and discusses the qualitative features of dark energy in modified gravity. The review critically examines the possibility of unifying inflation with the dark energy era using modified gravity. Additionally, the paper addresses astrophysical solutions in modified gravity, such as neutron and quark stars, black holes, and wormholes. The review aims to provide a comprehensive "toolbox" of modified gravity techniques for studying inflation, dark energy, and bouncing cosmologies. The paper highlights the importance of ensuring that modified gravity theories are consistent with both local and global observational constraints and that they provide a self-consistent framework for describing both early and late-time cosmic evolution. The review also discusses the challenges and obstacles in developing viable modified gravity theories and their potential to explain the observed accelerated expansion of the universe.Modified gravity theories are reviewed in the context of inflation, dark energy, and bouncing cosmology. The paper discusses various modified gravity frameworks, including $ F(R) $, $ F(\mathcal{G}) $, and $ F(T) $ gravity, as well as alternative theories. These theories are analyzed for their viability in describing the early universe's inflationary era, the late-time dark energy era, and bouncing cosmologies. The paper emphasizes the formalism of these theories and their ability to produce a viable inflationary era consistent with observational data. It also explores how bouncing cosmologies can be described within these frameworks and discusses the qualitative features of dark energy in modified gravity. The review critically examines the possibility of unifying inflation with the dark energy era using modified gravity. Additionally, the paper addresses astrophysical solutions in modified gravity, such as neutron and quark stars, black holes, and wormholes. The review aims to provide a comprehensive "toolbox" of modified gravity techniques for studying inflation, dark energy, and bouncing cosmologies. The paper highlights the importance of ensuring that modified gravity theories are consistent with both local and global observational constraints and that they provide a self-consistent framework for describing both early and late-time cosmic evolution. The review also discusses the challenges and obstacles in developing viable modified gravity theories and their potential to explain the observed accelerated expansion of the universe.