In this thesis we study the dynamics of the CDR3 loops of the T cell receptor (TCR). The TCR is the protein responsible for mediating the recognition of signs of infection in the T cell, a cornerstone of the adaptive immune system. The CDR loops are responsible for this recognition process, and years of crystallographic work have shed immense light on their interactions with antigens. However, the dynamics remain difficult to study, and the relationship between the flexibility of the loops, their motions, and their interaction with antigen is still poorly understood. Here, we have simulated the dynamics of two different TCR systems with molecular dynamics, and applied machine learning and signal processing technologies to pull apart the dynamics. This thesis gives a detailed background the analytic methods, and then applies them to the dynamics of the 2C and NKT15 TCR clones. A central question of the thesis asks if the CDR3 loops are flexible in solution and whether they demonstrate stable conformations in the absence of the environment of an antigen the TCR recognizes. Our main results are that the loops demonstrate restricted, coherent motion in solution, and that there exist distinct, stable clusters of conformations, states, of the CDR3 loops. The system undergoes transitions between these distinct conformational clusters, and this transition can be described as Markov system, providing a high level view of the dynamics. Furthermore, the simulation captures known crystallographic bound states. Finally, we show evidence for more restricted and simplified CDR3 motions in the NKT15 TCR clone, which is a TCR with more `innate-like' behavior, in contrast to the more complex motion of the 2C clone's CDR3 loops, despite their similar architecture.