  The emergence of quantum theory at the beginning of 20$-th$ century has
changed our view of the microscopic world and has led to applications such as
quantum teleportation, quantum random number generation and quantum computation
to name a few, that could never have been realised using classical systems. One
such application that has attracted considerable attention lately is
device-independent (DI) certification of composite quantum systems. The basic
idea behind it is to treat a given device as a black box that given some input
generates an output, and then to verify whether it works as expected by only
studying the statistics generated by this device. The novelty of these
certification schemes lies in the fact that one can almost completely
characterise the device (up to certain equivalences) under minimal physically
well-motivated assumptions such as that the device is described using quantum
theory. The resource required in most of these certification schemes is quantum
non-locality. In this thesis, we construct schemes to device-independently
certify quantum states and quantum measurements in Hilbert spaces of arbitrary
dimension along with the optimal amount randomness that one can extract from
any quantum system of arbitrary dimension.
