Although the observations of filaments within molecular clouds have been 
reported since decades, only recently (mostly thanks to Herschel results) 
their presence has been recognised as a unique characteristic of the 
star-formation process.  As a consequence, characterising the physical 
properties of these filaments has been revealed as key to our understanding 
of the origin of the stars within molecular clouds.
The large majority of observational papers use the classical ``Ostriker'' 
profile as a benchmark to interpret observations. However, it is worth 
recalling the assumptions and limitations of this model: (i) filaments are 
assumed to be isothermal, (ii) they are not rotating, (iii) they are isolated, 
(iv) they can be modelled as cylindrical structures with infinite length, 
(v) their support against gravity comes solely from thermal pressure.  
In this talk I will reviews a number of observational results suggesting that 
none of the above assumptions can be considered valid. I will then show how to 
relax some of the above hypotheses in order to take into account evidences 
derived from observations. I will show how these modifications change the 
properties of the modelled filaments and I will compare the results of these 
calculations with key observations in star-forming filaments.