There’s an idea out there, proposed by people who support intelligent design, known as irreducible complexity. What they believe is that biological systems are too complex to have possibly evolved by chance. I disagree with them on their point of evolution, but I do believe they have a very valid observation about the complexity of biological systems.
A lot of people get overwhelmed when they think about the vastness of space, but when I think about the complexity of biological machinery, it almost makes me want to throw up. Take a look at this: Metabolic Pathways and Cellular and Molecular Processes.

Biological complexity reminds me of space for some reason.
These biochemical reactions and cellular functions are happening in basically every cell of your body, and are happening in almost every cell in almost every organism on this planet. And it’s just the tip of the iceberg…
I’ll back up for a second. It’s well known that we’re all composed of relatively few elements (carbon, oxygen, etc), but when we move to high-order biological systems there’s even less variety. There are proteins, nucleic acids, lipids, maybe a few other macromolecules, and these all have very simple basic building blocks. For example there are only four(or five) bases in nucleic acids that encode all our genetic information, and only 20 amino acids make up proteins.
So the code of life is only four bases, and the machines/raw material of life is made of 20 amino acids. Food chains, replication, biodiversity, species, intelligence, having arms, whatever. All of it is 4 bases and 20 amino acids. Doesn’t seem that bad.
The central dogma of molecular biology is generally taught in science classrooms everything. It’s the idea that one gene codes for one protein, and that RNA is the mediator. The human genome project showed that out of the ~3 billion DNA base pairs that make up our genetic blueprint, we have about ~30,000 genes that code for proteins (our genes are ~1-2% of our total genome). So 30,000 genes, 30,000 proteins, doesn’t seem that bad… right?
Nope. I don’t even know where to begin. I can give only a few examples.

Alternative Splicing
Alternative splicing: a gene is made of coding and noncoding regions, called exons and introns. Coding regions are the regions that get turned into proteins, and noncoding regions are there for other purposes. But the kicker is, when DNA gets turned into mRNA (messenger RNA, which is like a copy of the master blueprint used to build the protein), these coding regions aren’t all copied over. Depending on what coding regions are actually transcribed, you can get a variety of proteins from a single gene, all of which complex implications further downstream. If you find a gene that causes cancer, and you think “hey let’s just delete it,” you wouldn’t be just deleting one malfunctioning protein, you might wipe out hundreds.
Epigentics: Knowing the full code of the human genome means almost nothing (right now).

Supercoiled DNA - We don't fully know how the code is read
DNA is really long – stretched out it’s ~2-3 meters for a human – yet it has to fit into the nucleus of every cell. It can do so because of an ultra-efficient storage method, where the DNA strands get super-coiled (imagine twisting a piece of rope). For genes to get expressed, the regions containing genes have to be uncoiled so that enzymes can get in there and do their work. The regulatory mechanisms for what areas get uncoiled are very complex, and have a heavy environmental affect – it’s one of the reasons why identical twins aren’t perfect copies of each other. There’s no change to the blueprint, but how it’s read is complicated.
Signaling pathways: Most biological functions in a cell, including gene expression, are initiated by a really complicated network of protein cascades.

Yikes
An example of this would be: A molecule on the outside of a cell is recognized by a protein on the membrane of the cell. That protein activates/changes another protein. Which activates/changes another protein. Which activates/changes a couple of other proteins. Which activates/changes other proteins. Which either do something or activate a gene that makes other proteins. Etc.
Cells cross talk, sending signals to each other (even by distance) and the network of inter- and intra-cellular communications is not an easy thing to study. We know a lot about these signaling pathways, but most of the research being done is piecing it together step by step… is this protein downstream or upstream of this one, what about that protein, what gene does this target, etc. It’s complicated.

Unraveling the tangle, thread by thread - that's science
Knowing all this, why would anyone ever want to study this stuff? I asked Dr. Marco Petrillo, a postdoc at Harvard Medical School who does research in signalling pathways in zebrafish, how he felt about the magnitude of complexity in what he was studying. “I want to quit my job,” was his immediate tongue-in-cheek reaction. “But it just means there’s more for us to discover, and that’s exciting,” he said after a little more thought.