Annotated text corpora facilitate the linguistic investigation of language as well as the automation of natural language processing (NLP) tasks. NLP tasks include problems such as spam email detection, grammatical analysis, and identifying mentions of people, places, and events in text. However, constructing high quality annotated corpora can be expensive. Cost can be reduced by employing low-cost internet workers in a practice known as crowdsourcing, but the resulting annotations are often inaccurate, decreasing the usefulness of a corpus. This inaccuracy is typically mitigated by collecting multiple redundant judgments and aggregating them (e.g., via majority vote) to produce high quality consensus answers. We improve the quality of consensus labels inferred from imperfect annotations in a number of ways. We show that transfer learning can be used to derive benefit from out-dated annotations which would typically be discarded. We show that, contrary to popular preference, annotation aggregation models that take a generative data modeling approach tend to outperform those that take a condition approach. We leverage this insight to develop csLDA, a novel annotation aggregation model that improves on the state of the art for a variety of annotation tasks. When data does not permit generative data modeling, we identify a conditional data modeling approach based on vector-space text representations that achieves state-of-the-art results on several unusual semantic annotation tasks. Finally, we identify a family of models capable of aggregating annotation data containing heterogenous annotation types such as label frequencies and labeled features. We present a multiannotator active learning algorithm for this model family that jointly selects an annotator, data items, and annotation type.