The universe is full of stuff we cannot see, neither directly or indirectly. We do not understand the nature of the mysterious dark matter and how it interacts with normal matter. Big Bang Nucleosynthesis (BBN) provides one of the major evidences for the standard model of cosmology, but important questions are yet to be answered. Using known physics we are able to predict most of the light element abundances we observe in the universe today. However, large uncertainties are present, and there is a major discrepancy between the predicted and observed abundance of lithium-7, known as the lithium problem. Moreover, we are confident that the standard model of particle physics is not complete. The question is whether or not extensions to this model, and in particular extensions involving the elusive dark matter, may alter the conditions during BBN. With high precision observations we need high precision predictions, thus the task of predicting the primordial element abundances relies heavily on precisely measured reaction rates and accurate numerical modeling. In this thesis I present an updated AlterBBN, a public available code for predicting the light element abundances with percentage precision. It has been modified to include generic dark matter candidates, and I analyze the effect of light WIMPs with a non-vanishing constant chemical potential. The general trend of the results is an increase in the lithium-7 abundance, extending the gap between the predicted and observed value, as well as an increased favoring of neutrino coupled WIMPs compared to previous studies where the chemical potential have been neglected. I have also made additional changes to the code, including an extension of the nuclear network and an update of six important reaction rates. This have lowered the deuterium yield by ∼ 4.5%, now being 2.456 ± 0.057 · 10^-5 , but still within the presently suggested observational constraint. Also here we see an increase in the lithium-7 abundance. Finding accurate estimates on the primordial abundances from an observational point of view is not a trivial task. The elements have evolved since BBN ended, as they have been produced and destroyed in stars and other astrophysical processes. The primordial deuterium abundance is an important tracer for the conditions during BBN, and we are able to obtain precise estimates of it by analyzing absorption features in gas clouds in the line of sight to distant quasars. However, extrapolating back to zero metallicity imposes systematic uncertainties, and for a statistically significant estimate we need many measurements. Using the Absorption LIne Software ALIS I have conducted a measurement of the deuterium abundance, based on an analysis of the absorption system towards the quasar Q1009+2956 at redshift z = 2.407. This is an ongoing process and is yet to be finished. I present in this thesis the present status of the work, as well as a PYTHON program I have written as an add-on to ALIS. This program creates composite spectra and models for a better representation of the results from ALIS, compared to its inbuilt plotting environment.