Machine Learning and Inference methods have become ubiquitous in our attempt to induce more abstract representations of natural language text, visual scenes, and other messy, naturally occurring data, and support decisions that depend on it. However, learning models for these tasks is difficult partly because generating the necessary supervision signals for it is costly and does not scale. This paper describes several learning paradigms that are designed to alleviate the supervision bottleneck. It will illustrate their benefit in the context of multiple problems, all pertaining to inducing various levels of semantic representations from text. In particular, we discuss (i) esponse Driven Learning of models, a learning protocol that supports inducing meaning representations simply by observing the model's behavior in its environment, (ii) the exploitation of Incidental Supervision signals that exist in the data, independently of the task at hand, to learn models that identify and classify semantic predicates, and (iii) the use of weak supervision to combine simple models to support global decisions where joint supervision is not available.