There had been a long tradition of belief, dating back to Aristotle, in the Spontaneous Generation of life. However, in 1862, only three years after the publication of The Origin of Species, Louis Pasteur published the results of work which conclusively refuted the theory that micro-organisms could arise spontaneously from organic substances. Thus, at the same time as the debate over Natural Selection was raging, it had become no longer possible to believe in the Spontaneous Generation of life, and so attention began to focus on the origin of the first organisms.
The key processes required for Evolution are Reproduction, Variation, Heredity, Competition and Natural Selection. Although the specific mechanisms underlying Reproduction, Variation and Heredity were not understood in Darwin and Wallace's time, their insight was to observe these processes, along with Competition, and to see that Natural Selection and Evolution take place as a logical consequence.
The theory of Evolution continues to be developed, and there is debate over some aspects (such as the concept of Punctuated Equilibrium), but our understanding today is the same in its major respects as that described in The Origin of Species. We have good reason to believe that all organisms alive on the Earth today are descended from a Common Ancestor, and we can see how such an organism could give rise to the diversity and complexity of life we see today.
The question for those interested in the Origin of Life today is therefore not to do with how the process of evolution operates; it is to do with how it started. In particular: How did the processes of Reproduction, Variation and Heredity originate? What was the nature of the first evolving entities, and how did they arise?