In a structured prediction problem, one needs to learn a predictor that, given a structured input, produces a structured object, such as a sequence, tree, or clustering output. Prototypical structured prediction tasks include part-of-speech tagging (predicting POS tag sequence for an input sentence) and semantic segmentation of images (predicting semantic labels for pixels of an input image). Unlike simple classification problems, here there is a need to assign values to multiple output variables accounting for the dependencies between them. Consequently, the prediction step itself (aka ``inference" or ``decoding") is computationally-expensive, and so is the learning process, that typically requires making predictions as part of it. The key learning and inference challenge is due to the exponential size of the structured output space and depend on its complexity. In this paper, we present a unifying perspective of the different frameworks that address structured prediction problems and compare them in terms of their strengths and weaknesses. We also discuss important research directions including integration of deep learning advances into structured prediction, and learning from weakly supervised signals and active querying to overcome the challenges of building structured predictors from small amount of labeled data.