Strolling with a skeptical biochemist
Serious criticisms of evolutionary theory have been floating around for half a century. The main focus is over the Modern Synthesis and whether it's the best explanation of evolution. That requires a throrough understanding of what the Modern Synthesis actually means and how it's understood by most evolutionary biologists.
One view is that the Modern Synthesis is almost exclusively about natural selection. If that's true, then Stephen Jay Gould makes a good case when he argues that the Modern Synthesis is effectively dead—it was killed off by the neutral theory and the recognition that random genetic drift is a major player in evolution [ Is the Modern Synthesis effectively dead? ].