Humans have always used sketches to explain the visual world. It is a simple and straight- forward mean to communicate new ideas and designs. Consequently, as in almost every aspect of our modern life, the relatively recent major developments in computer science have highly contributed to enhancing individual sketching experience. The literature of sketch related research has witnessed seminal advancements and a large body of interest- ing work. Following up with this rich literature, this dissertation provides a holistic study on sketches through three proposed novel models including sketch analysis, transfer, and geometric representation. The first part of the dissertation targets sketch authorship recognition and analysis of sketches. It provides answers to the following questions: Are simple strokes unique to the artist or designer who renders them? If so, can this idea be used to identify authorship or to classify artistic drawings? The proposed stroke authorship recognition approach is a novel method that distinguishes the authorship of 2D digitized drawings. This method converts a drawing into a histogram of stroke attributes that is discriminative of authorship. Extensive classification experiments on a large variety of datasets are conducted to validate the ability of the proposed techniques to distinguish unique authorship of artists and designers. The second part of the dissertation is concerned with sketch style transfer from one free- hand drawing to another. The proposed method exploits techniques from multi-disciplinary areas including geometrical modeling and image processing. It consists of two methods of transfer: stroke-style and brush-style transfer. (1) Stroke-style transfer aims to transfer the style of the input sketch at the stroke level to the style encountered in other sketches by other artists. This is done by modifying all the parametric stroke segments in the input, so as to minimize a global stroke-level distance between the input and target styles. (2) Brush-style transfer, on the other hand, focuses on transferring a unique brush look of a line drawing to the input sketch. In this transfer stage, we use an automatically constructed input brush dictionary to infer which sparse set of input brush elements are used at each location of the input sketch. Then, a one-to-one mapping between input and target brush elements is learned by sparsely encoding the target sketch with the input brush dictionary. The last part of the dissertation targets a geometric representation of sketches, which is vital in enabling automatic sketch analysis, synthesis and manipulation. It is based on utilizing the well known convolutional sparse coding (CSC) model. We observe that CSC is closely related to how line sketches are drawn. This process can be approximated as the sparse spatial localization of a number of typical basic strokes, which in turn can be cast as a non-standard CSC model that forms a line drawing from parametric curves. These curves are learned to optimize the fit between the model and a specific set of line drawings. Each part of the dissertation shows the utility of the proposed methods through a variety of experiments, user studies, and proposed applications.