Linear classification is a useful tool in machine learning and data mining. For some data in a rich dimensional space, the prediction performance of linear classifiers has shown to be close to that of nonlinear classifiers such as kernel methods, but training and testing speed is much faster. Recently, many research works have proposed efficient optimization methods to construct linear classifiers. We briefly discuss some of them that were considered in our development of the software LIBLINEAR. We then move to discuss some extensions of linear classification. In particular, linear classifiers can be useful to either directly or indirectly approximate kernel classifiers. I will show some real-word examples for which we try to achieve fast training/testing speed, while maintain competitive accuracy. Finally, future challenges of this research topic, in particular, aspects on big-data linear classification, will be discussed.