  Landscape functions are a popular tool used to provide upper bounds for
eigenvectors of Schr\"odinger operators on domains. We review some known
results obtained in the last ten years, unify several approaches used to
achieve such bounds, and extend their scope to a large class of linear and
nonlinear operators. We also use landscape functions to derive lower estimates
on the principal eigenvalue -- much in the spirit of earlier results by
Donsker-Varadhan and Ba\~nuelos-Carrol -- as well as upper bounds on heat
kernels. Our methods solely rely on order properties of operators: we devote
special attention to the case where the relevant operators enjoy various forms
of elliptic or parabolic maximum principles. Additionally, we illustrate our
findings with several examples, including p-Laplacians on domains and graphs as
well as Schr\"odinger operators with magnetic and electric potential, also by
means of elementary numerical experiments.
