One of the primary goals in modern physics is to answer the question "What is the Universe made of?" Often that question reduces to "What is matter and what holds it together?" This continues the line of investigation started by Democritus, Dalton and Rutherford.
Modern physics speaks of fundamental building blocks of Nature, where fundamental takes on a reductionist meaning of simple and structureless. Many of the particles we have discussed so far appear simple in their properties. All electrons have the exact same characteristics (mass, charge, etc.), so we call an electron fundamental because they are all non-unique.
Thus, our current understanding of the structure of the atom is shown below, the atom contains a nucleus surrounded by a cloud of negatively charged electrons. The nucleus is composed of neutral neutrons and positively charged protons. The opposite charge of the electron and proton binds the atom together with electromagnetic forces.
The protons and neutrons are composed of up and down quarks whose fractional charges (2/3 and -1/3) combine to produce the 0 or +1 charge of the proton and neutron. The nucleus is bound together by the nuclear strong force (that overcomes the electromagnetic repulsion of like-charged protons)