Similarity-based search of sequence collections is a core task in bioinformatics, one dominated for most of the genomic era by exact and heuristic alignment-based algorithms. However, even efficient heuristics such as BLAST may not scale to the data sets now emerging, motivating a range of alignment-free alternatives exploiting the underlying lexical structure of each sequence. In this paper, we introduce two supervised approaches-SuperVec and SuperVecX-to learn sequence embeddings. These methods extend earlier Representation Learning (RepL) based methods to include class-related information for each sequence during training. Including class information ensures that related sequence fragments have proximal representations in the target space, better reflecting the structure of the domain. We show the quality of the embeddings learned through these methods on (i) sequence retrieval and (ii) classification tasks. We also propose an hierarchical tree-based approach specifically designed for the sequence retrieval problem. The resulting methods, which we term H-SuperVec or H-SuperVecX, according to their respective use of SuperVec or SuperVecX, learn embeddings across a range of feature spaces based on exclusive and exhaustive subsets of the class labels. Experiments show that the proposed methods perform better for retrieval and classification tasks over existing (unsupervised) RepL-based approaches. Further, the new methods are an order of magnitude faster than BLAST for the database retrieval task, supporting hybrid approaches that rapidly filter the collection so that only potentially relevant records remain. Such filtering of the original database allows slower but more accurate methods to be executed quickly over a far smaller dataset. Thus, we may achieve faster query processing and higher precision than before.