What happens to electrons in metal complexes after excitation by visible light?
Absorption of a photon typically results in a vibrationally excited higher electronic state of the same multiplicity. 

$$\ce{S_0 -&gt;[$h\nu_\mathrm{ex}$] S_1}$$

In most cases, the excited state deactivates through internal conversion in a radiationless process via vibrational energy exchange with solvent molecules. No light is emitted here, but the solvent is actually heated up, although it might not be measurable.

There are however cases, in which the initially formed excited singlet state species first relaxes to its lowest vibrational mode and then emits a photon to reach the ground state. 

$$\ce{S_1 -&gt; S_0 + $h\nu_\mathrm{f}$}$$

This deactivation via radiation is known as fluorescence. Fluorescence lifetimes are typically rather short (in the ns range) and the emitted photon has a lower energy than the absorbed one. This means that the emission spectrum is shifted to the red end of the uv spectrum ($\lambda_\mathrm{f} &gt; \lambda_\mathrm{ex}$). The effect is known as Stokes shift.

A classical case for a fluorescent transition metal complex is $\ce{Ru(bpy)3^{2+}}$. 

In acetonitrile, it absorbs around $\lambda_\mathrm{ex} = 460~\mathrm{nm}$. The fluorescence is observed around $\lambda_\mathrm{em} = 620~\mathrm{nm}$.



Other bidentate ligands - more rigid than 2,2'-bipyridine (bpy) - often used are 1,10-phenanthroline (phen), dipyrido-[3,2-a:2',3'-c]phenazine (dppz), and benzo[i]dipyrido-[3,2-a:2',3'-c]phenazine (dppn).



In other cases, the excited singlet state undergoes a change in the spin multiplicity (Intersystem crossing) to a triplet state.

$$\ce{S_1 -&gt;[ISC] T_1}$$

These excited triplet states are usually much longer-lived. When they eventually deactivate via emission of a photon, this process is known as phosphorescence.

$$\ce{T_1 -&gt; S_0 + $h\nu_\mathrm{p}$}$$



Keeping all these processes in mind, one question arises - particular from younger students or pupils:

If our metal complex absorbs a photon and forms an excited state with such a short lifetime, why can we see a nevertheless observe permanent colour?

The answer is in the enormous numbers! 

Continuous irradiation with white light means that we send a huge number of photons. Moreover, the solution of our transition metal complexes in a cuvette (or a test tube) also contains more than one molecule. In fact, much more!

As a result, we have a huge number of incidents 


The complex absorbs a photon of a certain energy, which means that one colour is "swallowed". The complex forms a short-lived "excited state"
the solution reflects the remaining light
the excited state complex deactivates again


Since this happens all the time while we shine the light on our sample and for a lot of molecules, we observe a summary of the events: a coloured solution.