  Transport problems arise across diverse fields of science and engineering.
Semi-Lagrangian (SL) discontinuous Galerkin (DG) methods are a class of high
order deterministic transport solvers that enjoy advantages of both SL approach
and DG spatial discretization. In this paper, we review existing SLDG methods
to date and compare numerical their performances. In particular, we make a
comparison between the splitting and non-splitting SLDG methods for
multi-dimensional transport simulations. Through extensive numerical results,
we offer a practical guide for choosing optimal SLDG solvers for linear and
nonlinear transport simulations.
