Support vector machines (SVMs) have played a key role in broad classes of problems arising in various fields. Much more recently, SVMs have become the tool of choice for problems arising in data classification and mining. This paper emphasizes some recent developments that the author and his colleagues have contributed to such as: generalized SVMs (a very general mathematical programming framework for SVMs), smooth SVMs (a smooth nonlinear equation representation of SVMs solvable by a fast Newton method), Lagrangian SVMs (an unconstrained Lagrangian representation of SVMs leading to an extremely simple iterative scheme capable of solving classification problems with millions of points) and reduced SVMs (a rectangular kernel classifier that utilizes as little as 1% of the data).