  We address L\'{e}vy-stable stochastic processes in bounded domains, with a
focus on a discrimination between inequivalent proposals for what a boundary
data-respecting fractional Laplacian (and thence the induced random process)
should actually be. Versions considered are: restricted Dirichlet, spectral
Dirichlet and regional (censored) fractional Laplacians. The affiliated random
processes comprise: killed, reflected and conditioned L\'{e}vy flights, in
particular those with an infinite life-time. The related concept of
quasi-stationary distributions is briefly mentioned.
