RNA polymerase is central in gene transcription. During transcription elongation stage, the RNA polymerase processively adds nucleotides to a nascent RNA transcript based on a DNA template. The series of steps required to add a nucleotide are known as the nucleotide addition cycle (NAC). Multiple structural studies have provided static snapshots of the different steps of the NAC, however, the dynamical mechanisms connecting the steps remain elusive or controversial. Molecular Dynamics simulations are useful to study the function of biological molecules at atomic resolution, and in combination with Markov State Models (MSM), it is possible to reach long timescale dynamics, which are necessary to study the relevant steps of transcription elongation. This thesis presents the results obtained from extensive MD simulations and MSMs for: Trigger Loop Motion, Backtracking, Translocation (in eukaryotes) and Pyrophosphate Ion release (in a bacteria). A chapter is included regarding the construction of system that contains the full transcription bubble and the investigation of the possible NTP entry pathways. All these projects, taken together, provide a working model of the complete NAC at atomic resolution and at the millisecond timescale.