<p>Spectral retrieval is a key computational tool for interpreting spectroscopic observations of exoplanets. As data quality has dramatically improved with the launch of JWST, so the complexity of retrieval models has also increased. Due to the lack of ground truth and prior knowledge for exoplanets, retrievals adopt algorithms capable of exploring a wide parameter space, such as MCMC or Nested Sampling, which become increasingly inefficient for higher dimensionality problems. Tuning retrieval complexity for these scenarios requires a delicate compromise between sufficient physical accuracy and pragmatic approximations. Retrievals can be applied to many different types of observation, with specific challenges associated with each. In the current environment, as we begin characterize smaller, temperate planets that may potentially be habitable, interpretation of retrievals and calculation of detection significance must be approached with special care. In this review, we summarize the current computational challenges in all aspects of the retrieval process: atmospheric modelling; data preparation; inversion and likelihood calculation; and interpretation, for a range of observational strategies. We conclude with a series of recommendations for scientists approaching retrievals for the first time in this new data-rich era for exoplanet science.</p>