Albert Einstein taught us that gravity should be understood as curvature of space. In the context of General Relativity, this is done using symmetric connection formalism. There is an alternative formalism known as 'teleparallel gravity' where we interpret gravity as torsion of space. In this book, we study several generalizations and applications of teleparallel gravity specially to solve the Dark Energy and Dark Matter problems of modern cosmology. This book is based on our collected works in this field.