  Vector-boson fusion and vector-boson scattering are an important class of
processes for the Large Hadron Collider at CERN. It is characterized by two
high-energetic jets in the forward regions of the detector and reduced jet
activity in the central region. The higher center-of-mass energy during the
current and subsequent runs strongly boosts the sensitivity in these processes
and allows to test the predictions of the Standard Model to a high precision.
  In this review, we first present the main phenomenological features of
vector-boson fusion and scattering processes. Then we discuss the effects of
higher-order corrections, which are available at NLO QCD for all processes and
up to N3LO QCD and NLO electro-weak for VBF-H production. An additional
refinement is the addition of parton-shower effects, where recently a lot of
progress has been made. The appearance of triple and quartic gauge vertices in
the production processes enables us to probe anomalous gauge couplings. We
introduce and compare the different parametrizations used in the literature and
also discuss the issue of unitarity violation and common unitarization
procedures. Finally, we give a short overview of current and possible future
experimental searches.
