  The late time acceleration of the Universe has challenged contemporary
cosmology since its discovery. General Relativity explains this phenomenon by
introducing the cosmological constant, named the standard cosmological model
($\Lambda$CDM). However, the cosmological constant solution has several
drawbacks that have led cosmologists to explore and propose alternative models
to explain the late time acceleration of the Universe. These alternatives span
from models of a dynamical dark fluid, known as dark energy, to models of
large-scale modifications of the gravitational interaction, known as modified
gravity. The current dissertation intends to show several ways to investigate
late-time cosmology or to look at probable places for future investigations in
order to shed more light on the dark sector of the Universe...
