1. Radioactive Decay
For every element, there exist different kinds of isotopes; so there exist versions with different numbers of neutrons. If the number of neutrons gets too low or too high, the nulceus becomes unstable. That means that the nucleus may spontanously decay (zerfallen).
Example: 12C is stable. 14C is not.
Furthermore, there no stable nulcei (nuclides) with more than 82 protons exist.
The decay of nuclei are called radioactivity!

2. Alpha (α) decay
Some nuclei with an unstable combination of neutrons and protons can get rid of some neutrons and protons by sending out an α-particle (4He):
In an α-decay A and Z are conserved.
Decays occur, because the process releases energy!

3. Beta (β-) decay
In other cases, where there are too many neutrons, it is energetically favourable for the nucleus to convert a neutron into a proton:
A is conserved, but Z increases by 1, while N decreases by 1. The total charge is conserved.

4. Gamma (γ) radiation
Finally, if the nucleus has too much energy, it can get rid of this by sending out a photon called an γ-ray, just as the electrons can send out light, when they jump to an orbital with lower energy.

5. Nuclear Decay Series
When the mother nucleus decays, the daughter nucleus is not necessarily stable. It may itself spontanously decay.

6. Beta (β+) decay
If there are too few neutrons, a proton can be converted into a neutron.
A is conserved, but Z decreases by 1, while N increases by 1. The total charge is conserved.

7. Electron Capture
Alternatively to the β+ decay, the nucleus may capture one of the orbiting electrons, and the electron turns a proton into a neutron:
A is conserved, but Z increases by 1, while N decreases by 1. The total charge is conserved.