pointwise convergence of Fourier series

I am a bit confused. I have heard today someone saying that the Fourier series of any continues periodic function $f$, say with period 1 for concreteness, converges pointwise to $f$. Wikipedia here explicitly says otherwise, but claims that the proof is not constructive and somewhat advanced. So what is it?

I have to apologize for this question, since I could just pick any book about Fourier analysis and check it up myself, but since the answer is a simple "yes" or "no" I hope it is not to much of an effort to answer this for someone how knows the answer.

See Theorem 2.2 in this pdf which shows (the proof is not really complete) that there is a continuous periodic function with divergent fourier series in some point. The first example of such a function was given by DuBois-Reymond in 1873, in the meantime this has even been extended (see the note on page 13):

For every null set $N \subset ]-\pi,\pi]$ there is a continuous periodic function for which the Fourier series is divergent in each point of $N$.

Shown in Y. Katznelson, An introduction to harmonic analysis. Wiley 1968.