  Surrogate-assisted search-based testing (SA-SBT) aims to reduce the
computational time for testing compute-intensive systems. Surrogates enhance
testing techniques by improving test case generation focusing the testing
budget on the most critical portions of the input domain. In addition, they can
serve as approximations of the system under test (SUT) to predict tests'
results instead of executing the tests on compute-intensive SUTs. This article
reflects on the existing SA-SBT techniques, particularly those applied to
system-level testing and often facilitated using simulators or complex test
beds. Our objective is to synthesize different heuristic algorithms and
evaluation methods employed in existing SA-SBT techniques and present a
comprehensive view of SA-SBT solutions. In addition, by critically reviewing
our previous work on SA-SBT, we aim to identify the limitations in our proposed
algorithms and evaluation methods and to propose potential improvements. We
present a taxonomy that categorizes and contrasts existing SA-SBT solutions and
highlights key research gaps. To identify the evaluation challenges, we conduct
two replication studies of our past SA-SBT solutions: One study uses industrial
advanced driver assistance system (ADAS) and the other relies on a Simulink
model benchmark. We compare our results with those of the original studies and
identify the difficulties in evaluating SA-SBT techniques, including the impact
of different contextual factors on results generalization and the validity of
our evaluation metrics. Based on our taxonomy and replication studies, we
propose future research directions, including re-considerations in the current
evaluation metrics used for SA-SBT solutions, utilizing surrogates for fault
localization and repair in addition to testing, and creating frameworks for
large-scale experiments by applying SA-SBT to multiple SUTs and simulators.
