Modern Ab Initio Approaches and Applications in Few-Nucleon Physics with A \ge 4

We present an overview of the evolution of ab initio methods for few-nucleon systems with A \ge 4, tracing the progress made that today allows precision calculations for these systems. First a succinct description of the diverse approaches is given. In order to identify analogies and differences the methods are grouped according to different formulations of the quantum mechanical many-body problem. Various significant applications from the past and present are described. We discuss the results with emphasis on the developments following the original implementations of the approaches. In particular we highlight benchmark results which represent important milestones towards setting an ever growing standard for theoretical calculations. This is relevant for meaningful comparisons with experimental data. Such comparisons may reveal whether a specific force model is appropriate for the description of nuclear dynamics.Comment: extension of the previous version from 70 to 78 pages, 24 figures, 17 tables, in press: Progress in Particle and Nuclear Physic