SED fitting is the practice of inferring physical properties of a stellar population (a galaxy, a cluster...) from measures of the Spectral Energy Distribution.
The spectrum of a stellar population is extremely information rich. It can be used to infer age, redshift, metallicity, present and past star formation rate, total stellar, dust and gas mass, as well as the relative proportion of the different kind of stars.
In order to infer these parameters, one needs a software that is able, given the parameters, to generate (synthesize) a template spectrum. The template spectrum is then compared to the measured spectrum. The software is also able to search the parameters space in order to find the set of parameters that provide a spectrum that is the most similar to the measured one. Some softwares search for the parameters that minimize the $\chi^2$ of the data, others provide a full Bayesian analysis of the parameter space.
The center of the diagram contains the name of different popular SED fitting softwares. A longer and more comprehensive list can be found at http://www.sedfitting.org/Fitting.html.
How to synthesize a SED
A synthetic SED must take into account many aspects that can influence the spectrum of a stellar population. Different studies give different prescriptions about the treatment of these phenomena. The outer ring of the picture presents some of the most popular prescriptions and link them with the SED fitters that use them. In this sense, the figure is a quick reference to see what each software is taking into account. One expert that works in the field will know at a glance the pros and cons of every prescription, and will be able to select the SED fitter according to their present needs.
As a first approximation, the SED of a stellar population is the sum of the spectra of the single stars. It then goes without saying that a SED fitting software will need a stellar spectra library. Synthesizing the spectrum of a single star is a very complicated task. Authors of SED fitters don't usually roll their own stellar spectra generators, but use other public software. These codes provide a library of precomputed stellar spectra, for different ages and metallicity.
Initial mass function
Not all stars are created equal. When stars form, some are more massive and others are lighter. Different masses will lead to extremely different lives and spectra. When $100 M_\odot$ of gas convert into newborn stars, the SED fitter needs to decide how this mass is distributed among the stars. For example, we know that the majority of stars have $M \le 1M_\odot$ and very few stars have $M>10M_\odot$. The initial mass function (IMF) is the distribution of masses among a newborn stellar population.
In the figure there are some of the most popular IMFs, reported with the name of the first author of the paper that proposed them. They usually consist of power laws, or broken power laws.
Star formation History
Were all the stars born in a single burst, like in a globular cluster? Or did they form more slowly? In repeated bursts? Is the star formation still going on now? These questions are answered by the star formation history function, that gives the star formation rate (solar masses per year) as a function of time since the birth of the first stars until now. Young stars have a very different spectrum than old ones, therefore when generating a SED it is important to keep track of the different ages of the stars in the stellar population.
Dust attenuation and emission
The presence of dust can significantly alter the shape of a SED. Dust particles absorb visible and UV light, and emit the energy back in the infrared. Different models have been proposed to take care of the effect of dust on a SED.
If the galaxy contains an Active Galactic Nucleus, it is fundamental to include it in the synthetic SED. The flux of the AGN can single-handedly exceed the flux of the whole galaxy. Again, different AGN templates can be used.
The metallicity of a star greatly influences its spectrum. The metallicity of a star is usually taken to be equal to the metallicity of the gas from which the star formed. In the early universe the metallicity of the gas was low, but stars produce metals and release them to the interstellar medium, therefore the second generation of stars will tend to have a greater metallicity, and so on. A SED fitter may choose to ignore this fact, and keep the metallicity constant (for example if it is specialized on single burst populations), or may try to model the varying metallicity in a more complicated way.
A SED fitter may choose to take into account a detailed treatment of emission lines from H2 regions, planetary nebulae, supernovae, interstellar, circumstellar, and intergalatic medium etc...
Some SED fitters are extend their focus on some extreme part of the EM spectrum (most of them typically only treat IR-visible-UV) like radio or X-ray.