This thesis investigates models of dark energy based on generalized theories in the framework of the teleparallel equivalent of general relativity. We study the cosmic background evolution in the quintessence-inspired teleparallel dark energy model. We explore the cosmological perturbation of $f(T)$ gravity, and we analyze the similar perturbation scenario of teleparallel quintessence model. We check the viability of teleparallel dark energy theories in the weak-field regime through the parametrized post-Newtonian approach, and finally, we show that the Cauchy problem in the generalized teleparallel theory can be resolved by a time-gauge fixing condition.