  One of the most fundamental phenomena of quantum physics is entanglement. It
describes an inseparable connection between quantum systems, and properties
thereof. In a quantum mechanical description even systems far apart from each
other can share a common state. This entanglement of the subsystems, although
arising from mathematical principles, is no mere abstract concept, but can be
tested in experiment, and be utilized in modern quantum information theory
procedures, such as quantum teleportation. In particular, entangled states play
a crucial role in testing our understanding of reality, by violating Bell
inequalities. While the role of entanglement is well studied in the realm of
nonrelativistic quantum mechanics, its significance in a relativistic quantum
theory is a relatively new field of interest. In this work the consequences of
a relativistic description of quantum entanglement are discussed. We analyze
the representations of the symmetry groups of special relativity, i.e. of the
Lorentz group, and the Poincar\'e group, on the Hilbert space of states. We
describe how unitary, irreducible representations of the Poincar\'e group for
massive spin 1/2 particles are constructed from representations of Wigner's
little group. We then proceed to investigate the role of the Wigner rotations
in the transformation of quantum states under a change of inertial reference
frame. Considering different partitions of the Hilbert space of 2 particles, we
find that the entanglement of the quantum states appears different in different
inertial frames, depending on the form of the states, the chosen inertial
frames, and the particular choice of partition. It is explained, how, despite
of this, the maximally possible violation of Bell inequalities is frame
independent, when using appropriate spin observables, which are related to the
Pauli-Ljubanski vector, a Casimir operator of the Poincar\'e group.
