1 Introduction
2 Modelling galaxy SEDs
 2.1 Stars
  2.1.1 Simple stellar populations
  2.1.2 Validation of SSP predictions
  2.1.3 Current Issues with SSPs
 2.2 The ISM around the stars
  2.2.1 Interstellar gas
  2.2.2 Interstellar dust
  2.2.3 Combining stellar and dust emission
 2.3 Evolution of Galaxies
3 Constructing observed galaxy SEDs
 3.1 Spectral response curve and resolution
 3.2 Spatial resolution, aperture bias and matching
 3.3 Examples of multi-wavelength datasets
  3.3.1 The Spitzer Local Volume Legacy - spatially resolved SEDs
  3.3.2 The Herschel ATLAS - unresolved SEDs
  3.3.3 The SWIRE templates
  3.3.4 Further examples
4 Methods and validation of SED fitting
 4.1 Parametrizing SED models
 4.2 Spectral indices
 4.3 Principal Component Analysis
 4.4 Spectral fitting by inversion
  4.4.1 Method
  4.4.2 Non-linear inversion codes
  4.4.3 Non-linear physics
  4.4.4 Validation
 4.5 Bayesian inference
  4.5.1 Method
  4.5.2 Libraries and priors
  4.5.3 Validation
 4.6 Method-independent caveats
5 Results of SED Fitting: Photometric redshifts
 5.1 Methods
  5.1.1 Empirical techniques
  5.1.2 Template Fitting
 5.2 Calibration and error budgets
  5.2.1 Template accuracy
  5.2.2 Spectroscopic Calibration of Photo-zs
  5.2.3 Signal-to-noise Effects
 5.3 A unified framework
 5.4 The State of Photometric Redshifts
6 Results of SED Fitting: Physical Properties
 6.1 Stars
  6.1.1 Stellar masses
  6.1.2 Deriving SFHs from spectroscopy
  6.1.3 Identifying and studying outliers
 6.2 Dust
  6.2.1 Attenuation by Dust
  6.2.2 Dust Emission
  6.2.3 Dust in the UV to IR
  6.2.4 Star Formation Rate from the IR
 6.3 Fitting the full UV to FIR SED
7 Conclusions

Abstract Fitting the spectral energy distributions (SEDs) of galaxies is an almost universally used technique that has matured significantly in the last decade. Model predictions and fitting procedures have improved significantly over this time, attempting to keep up with the vastly increased volume and quality of available data. We review here the field of SED fitting, describing the modelling of ultraviolet to infrared galaxy SEDs, the creation of multiwavelength data sets, and the methods used to fit model SEDs to observed galaxy data sets. We touch upon the achievements and challenges in the major ingredients of SED fitting, with a special emphasis on describing the interplay between the quality of the available data, the quality of the available models, and the best fitting technique to use in order to obtain a realistic measurement as well as realistic uncertainties. We conclude that SED fitting can be used effectively to derive a range of physical properties of galaxies, such as redshift, stellar masses, star formation rates, dust masses, and metallicities, with care taken not to over-interpret the available data. Yet there still exist many issues such as estimating the age of the oldest stars in a galaxy, finer details of dust properties and dust-star geometry, and the influences of poorly understood, luminous stellar types and phases. The challenge for the coming years will be to improve both the models and the observational data sets to resolve these uncertainties. The present review will be made available on an interactive, moderated web page (, where the community can access and change the text. The intention is to expand the text and keep it up to date over the coming years.