Pre-Darwin biologist: "I can see that lots of animals (and fossils) are clearly similar to each other, and share anatomical features across even very distant taxa. Life certainly looks like it's evolved. The problem is, I just don't understand how a random process could have led to such exquisite adaptation: there must have been a Designer."
Darwin: "Hang on, I have an idea. If there are more offspring born each generation than survive to reproduce, then there must be a struggle between individuals for survival. And, if there is variation between individuals such that some individuals are inherently better equipped to survive and/or reproduce, then the result of this competition will be (to some extent) non-random and those individuals who are better adapted will have more offspring than those that are not. And, if there is inheritance of characteristics from parent to offspring, the next generation will be better adapted, on average, than the previous generation as a result. Aaaand, if variation is something that enters the population at each generation, this cycle will continue, resulting in more and more adapted individuals. Over many, many generations, exquisite adaptations can evolve."
Post-Darwin biologist: "Competition: check. Variation: check. Inheritance: check. Mutation: check. Genius! Not only is adaptation from random variation explained, it is hard to see how it could not happen! Well done, Darwin - an elegant solution to a tricky problem. All those oddities in nature make so much more sense, now."
Intelligent Design: "The problem is, I just don't understand how a random process could have led to such exquisite adaptation: there must have been a Designer."
Well done guys... Your big "problem" with Darwin is precisely the problem he elegantly solved 150 years ago. Bravo.