  Strong gravitational lenses provide unique laboratories for cosmological and
astrophysical investigations, but they must first be discovered - a task that
can be met with significant contamination by other astrophysical objects and
asterisms. Here we review strong lens searches, covering various sources
(quasars, galaxies, supernovae, FRBs, GRBs, and GWs), lenses (early- and
late-type galaxies, groups, and clusters), datasets (imaging, spectra, and
lightcurves), and wavelengths. We first present the physical characteristics of
the lens and source populations, highlighting relevant details for constructing
targeted searches. Search techniques are described based on the main lensing
feature that is required for the technique to work, namely one of: (i) an
associated magnification, (ii) multiple spatially-resolved images, (iii)
multiple redshifts, or (iv) a non-zero time delay between images. To use the
current lens samples for science, and for the design of future searches, we
list several selection biases that exist due to these discovery techniques. We
conclude by discussing the future of lens searches in upcoming surveys and the
new population of lenses that will be discovered.
