Ok, perhaps the question is in regard to atoms themselves separate from their incorporation into molecules.
There are several parts to this, (warning now I'm really becoming uncertain of how firm all this is):
1) Holding electrons around the nucleus.
This is also electromagnetic. The nucleus is positivly charged and electrons carry a negative charge.
2) Holding protons and neutrons together in the nucleus.
Since neutrons carry no charge and protons are positive the nucleus has an electromagnetic force pushing it apart. This is where the strong nuclear force comes in. The neutrons and protons are bound together by the strong force. (IIRC, bosons are the exchanged particle). There have to be enough neutrons in the nucleus to "balance" the protons. Smaller nuclei have equal numbers of protons and neutrons (generally). As the atomic number goes up it starts to take more than an equal number of neutrons to hold it together. Eventually a nucleus can't be held together even with a significant excess of neutrons ( e.g., Uranium 238 has 92 protons and 146 neutrons). These elements are always radioactive.
3) What holds the protons and neutrons together.
Gluons hold them together. Gluons, I think, might have been detected in the very latest "atom smasher" experiments. Protons and Neutrons are made of "quarks" ( a term from James Joyce IIRC).
That is probably as much detail as anyone could want. It is probably more than you wanted.
What you 'heard' is correct in that we don't know everything. But it is very, very wrong given the amount that is known about this stuff.