  The strong interaction between an antikaon and a nucleon is at the origin of
various interesting phenomena in kaon-nuclear systems. In particular, the
interaction in the isospin $I=0$ channel is sufficiently attractive to generate
a quasi-bound state, the $\Lambda(1405)$ resonance, below the $\bar{K}N$
threshold. Based on this picture, it may be expected that the $\bar{K}N$
interaction also generates quasi-bound states in kaon-nuclear systems,
sometimes called kaonic nuclei. At the same time, the $\bar{K}N$ quasi-bound
picture of the $\Lambda(1405)$ is also related to the discussion of hadronic
molecules in hadron spectroscopy. Here an overview is presented of the
theoretical studies developed for kaon-nucleon and kaon-nuclear systems. We
start from the modern understanding of the $\Lambda(1405)$ resonance. We then
discuss the $\bar{K}N$ interaction and various aspects of few-body kaonic
nuclei. Heavier kaon-nuclear systems are examined from the viewpoint of nuclear
many-body physics, with focus on the properties of antikaons in nuclear matter.
Related topics, such as the $K^{-}p$ momentum correlation functions in
high-energy collisions and the studies of kaonic atoms, are also discussed.
