Evolutionary theory has come a long way since Charles Darwin published On the Origin of Species in 1859. Prior to its publication, and in direct competition, Jean-Bapiste Lamarck was promulgating a well-known incorrect variant of evolutionary theory: Lamarckism or Lamarckian evolution. Lamarck thought that changes to the body over the course of a lifetime could be passed down to ancestors as long as they were common to both sexes of the species.
For instance, his explanation for why a giraffe has a long neck is because the giraffe had a history of predecessors that tried harder and harder to reach tall leaves on a tree, and accordingly the offspring were born with larger necks. This theory of evolution has been demonstrated to be false - the genetic difference between parents and offspring can be explained entirely by their genes, and requires no reference to the daily lives of the parents.
The most important theory of evolution is known as the modern synthesis or neo-Darwinian synthesis, which is the combination of Darwinian natural selection with Mendelian genetics and Thomas Morgan's chromosome theory of inheritance. This theory continues to be predominant to this day, with a few minor differences.
Mendel, a German monk who lived around the same time as Darwin but whose work was not rediscovered until 1900, experimented extensively with plants and found out the concepts of alleles (different versions of the same gene), dominant and recessive traits, and that the expression of different traits are exclusive to one another. Darwinian evolution and natural selection is just the idea that life evolves based on random mutations and selective pressures on individuals trying to reproduce.
In the 1960s, it became necessary to introduce the "gene-centric" view of natural selection, not really an independent theory but more of a footnote on the modern synthesis. Around this time, some biologists mistakenly were thinking that individuals evolve traits for the good of their species or the group.
To correct this, it was necessary to put forth a gene-centric view of evolution, where organisms as viewed as the "survival machines" of genes, only constructed for the sole purpose of passing those genes on. For example, a gene can opt for an organism with a shorter lifespan and faster reproductive cycle if that's what evolution selects for. The genes do not care about the well-being of their shells, the organism. This is probably the most sophisticated and recent iteration in the ongoing evolution of evolutionary theory.
