Randomness is a powerful resource in computer science, with rich applications in algorithm design, cryptography, distributed computing, etc. Most of the applications assume access to a sequence of uniform and independent random bits. However, the randomness we collect from nature (e.g., activity of CPU, atmospheric noise, ra-dioactive decay) does not seem as perfect. This motivates the study of randomness extractors, which are deterministic algorithms that can convert an imperfect random source (with some entropy) into a uniform random string. The ultimate goal in the area of randomness extraction is to construct an extractor that can work for any source that we would ever see in nature and applications. Unfortunately, a folklore result shows that it is impossible to construct an extractor that can work for every source that has entropy. It is therefore necessary to assume that the given source has certain structure, but we still hope that the structure we assume is as general as possible. In this thesis, we first focus on the construction of randomness extractors for sources with additive structure. This includes affine sources, which are uniform distributions over affine subspaces; and more generally the sum of two independent sources, which is a surprisingly general model that contains many other natural sources such as independent sources, affine sources and sources samplable by space-bounded computation. For both models, we construct extractors that improve the previous state-of-the-art, and develop many useful tools along the way. In addition, we discover new connections between sources with additive structure and space-bounded computation, and as a result we obtain extractors for small-space sources with optimal entropy requirement, and a new lower bound for linear branching programs. Finally, we develop more results regarding randomness and space-bounded computation, including new weighted pseudorandom generators and derandomization bounds for small-space algorithms.