Collecting samples that exhaust all possible classes for real-world tasks is usually difficult or impossible due to many different factors. In a realistic/feasible scenario, methods should be aware that the training data is incomplete and that not all knowledge is available. Therefore all developed methods should be able to identify the unknown samples while correctly executing the proposed task to the known classes in the tests phase. Open-Set Recognition and Semantic Segmentation models emerge to handle this kind of scenario for, respectively, visual recognition and dense labeling tasks. Initially, this work proposes a novel taxonomy aiming to organize the literature and provide an understanding of the theoretical trends that guided the existing approaches that may influence future methods. This work tested the proposed techniques on remote sensing data, establishing new state-of-the-art results for the used datasets. Remote sensing data differs from RGB data as it deals with a plethora of sensors and with a high geographical variation. Open set segmentation is a relatively new and unexplored task, with just a handful of methods proposed to model such tasks. This work also proposes two distinct techniques to perform open-set semantic segmentation. First, a method called OpenGMM extends the OpenPCS framework using a Gaussian Mixture of Models to model the distribution of pixels for each class in a multimodal manner. Second, the Conditional Reconstruction for Openset Semantic Segmentation (CoReSeg) method tackles the issue using classconditioned reconstruction of the input images according to their pixel-wise mask. CoReSeg conditions each input pixel to all known classes, expecting higher errors for pixels of unknown classes. Qualitative results observation suggested that both proposed methods produce better semantic consistency in their predictions than the baselines, resulting in cleaner segmentation maps that better fit object boundaries. Also, OpenGMM and CoReSeg outperformed state-of-the-art baseline methods on Vaihingen and Potsdam ISPRS datasets. The third proposed approach is a general post-processing procedure that uses superpixels to enforce highly homogeneous regions to behave equally, rectifying erroneous classified pixels within these regions. We also proposed a novel superpixel generation method called FuSC. All proposed approaches improved the quantitative and the qualitative results for both datasets. Besides that, CoReSeg s prediction post-processed with FuSC achieved state-of-the-art results for both datasets. The official implementation of all proposed approaches is available at https://github.com/iannunes.