The DNA molecule, apart from carrying the genetic information, plays a crucial role in a variety of biological processes and finds applications in drug design, nanotechnology and nanoelectronics. The molecule undergoes significant structural transitions under the influence of forces due to physiological and non-physiological environments. Here, we summarize the insights gained from simulations and single-molecule experiments on the structural transitions and mechanics of DNA under force, as well as its elastic properties, in various environmental conditions, and discuss appealing future directions.