Context :

Aims : We use different tracers , such as H \alpha , ultraviolet ( UV ) , and infrared ( IR ) emissions at various wavelengths , to study the dust and star-formation ( SF ) conditions throughout the disk of M 33 .

Methods : We derive the radial distribution of dust , of the old and young stellar population using Spitzer and GALEX data , complemented by ground-based optical data and available surveys of atomic and molecular gas .
We separate the contribution of discrete sources to the IR brightness from the diffuse emission .

Results : At 8 and 24 \mu m , discrete sources account for \gtrsim 40 % of the IR emission in the innermost 3 kpc , and for \lesssim 20 % further out .
We find that stochastic emission from very small grains in the diffuse interstellar medium accounts for only \sim 10 % of the diffuse 24 \mu m emission , and that dusty circumstellar shells of unresolved , evolved AGB stars ( carbon stars ) are a viable alternative .
The 8 \mu m profile suggests that PAH emission declines faster with radius than the dust continuum .
In annular regions , 0.24 kpc wide , we find a mean extinction value for stellar continuum A _ { V } \sim 0.25 mag with a weak dependence on radius , consistent with the shallow metallicity gradient observed .
Dust opacity derived from the 160 \mu m emission decreases instead by a factor 10 from the center to edge of the SF disk .

Conclusions : Using extinction corrected UV and H \alpha maps we find the global SF rate in M 33 , over the last 100 Myr , to be 0.45 \pm 0.10 M _ { \odot } yr ^ { -1 } .
FIR ( far-IR ) and TIR ( total-IR ) luminosities can trace SF even though a high conversion factor is required to recover the effective rate .
If carbon stars are powering the diffuse 24 \mu m emission in M 33 this can trace star formation 1 Gyr ago and provide a more complete view of the SF history of the galaxy .
Today the SF rate declines radially with a scale length of \sim 2 kpc , longer than for the old stellar population , suggesting an inside-out growth of the disk .