I would say that we live in reality and we perceive it through our senses.

Our senses are limited and our interpretation of the data we receive through our senses can at times be faulty (which makes illusions work).

We can to some degree compensate for the limitations using tools that can measure outside our limitations and for faulty interpretation through making many observations and tests.

All in all I believe our (humanity's) understanding of reality is fairly good on the level where we live. Individual members of humanity can however have a really bad understanding of reality.

Whether a baby is beautiful or not, is in the eye of the beholder. Has nothing to do with reality.

Yes, I guess you mean interpretation. Even though our eye interprets the World around you differently, we all see the same thing. Much like the same way the brain interprets our experience and senses.

They're connected. Reality shapes perception, perception is your particular idea of what reality is.

This is relevant: Conceptual Reality    My sensory connections are a bit wonky. Sometimes, when I hear someone speak, all I hear is noise. I do hear them, and I should know the words they're using, but in my brain something fails to translate what I hear into concepts. I can't even distinguish words as sounds separate from each other. Less often, it happens with my sight as well. I can see the colors and the shapes, but I don't know what it is, even if the object should be very familiar.
    I don't feel I can adequately describe what it feels like for something not to have a concept, to be unable to identify a stimulus. It's sort of like "what the fuck am I hearing/looking at?" confusion and frustration. Only no sense can be made of it until something clicks and then everything falls into place and I wonder why I couldn't recognize it without thinking.
    The things on my desk, in my room, even in my head, all have identities. They are not just random colors and shapes or bits of ideas and I wrote it some time ago.

In addition to the waves we can't see as pointed out by Underdell, we also can't always see beyond our own biases. Reality exists, but no one can fully see it.

Of course, our perception of reality is only a small percentage of the true form of reality. This is fact. 

We are unable to see countless spectrum colours, we can't see radio waves, radiation, magnetic waves, microwaves, etc. etc.

Our brains are only capable of deciphering a fragment of the true form of reality. There are certain things in our reality that grant us access to an augmented brain processing capability and unlock a truer perception of reality, but these are generally seen as hallucinogens, dismissed as a trick of the chemicals

About perception and reality I like the theory of a spanish philosopher, Ortega y Gasset, who says that reality is not distorted by our senses like other philosopher said. He believes that reality is a whole thing, like a polyhedron but who has infinite faces. Every face of the polyhedron is a point of view which belongs to a person. What happens with that? The thing is that this mean every one has a point of view of the reality, which represent reality for that person but is not reality in itself because in the point of view, that person see a limited reality. Reality in itself would be the joining togheter of all the different views, which will make a pure reality, "the truth", something which will never could be known by the human, cause we always are attached to our own point of view, limited by our personal circustances (our time context, place context and emotional context). That's what I usually think about reality.

Between perception and reality I prefer perception, because realityis something deep which I find we cannot truly reach, what reality is in the daily life is something we have create based in the common perpectives and agreement. 

We believe what we want to believe, but when others look at something, it becomes their perception and it's up to us to accept it or not.

However, when it comes to job interviews, your reality does not matter when it's their perception of you makes the difference if they're going to hire you or not.

Unless you give them statistical facts and proof, it's their words against yours. 

Perception is reality. Bare with me if I perceive like you that a baby is not cute mainly because of my autism, then for me in my reality babies aren't cute. I think reality is an individual thing rather than a corporate ever-changing event I hope I have explained myself fully in a way that is slightly understandable I am bad with words.

you need to look into phenomenology.  neat stuff.

I have moved this thread to the Philosophy and Religion Forum as it is better suited here.

It is not a secret that we live inside the matrix

interesting topic. Honestly tho, in a world where photoshop replaces photos & things like facebook replace friendships, I can't say that we live in full reality anymore

Both. It's inside and outside story.