There are any number of ways to look at gravestones. Quite obviously most genealogical researchers look at them to get names and dates (and don't we all hate the one with Mother and Father when that's all that they have!).
But sometimes digging deeper, no pun intended, can provide a look at the real people who had these stones created for them. Illustrations that come to mind are from a local college class on the symbolism of gravestone design and carvings. The students select ones that seem interesting and write up a biography of the people that are buried by the stones. In many cases, this proves to be very interesting. While they are doing this for college credit and do this research concerning strangers to them, you may find it very interesting to do the same kinds of lookups and see what secrets or interesting things have occurred in your own family backgrounds.
One student saw a gravestone shaped like a chair, and started look for more information. As it turned out, the couple buried there had children who are now still alive and that student interviewed them. The man had been a tailor and went off to World War I. His arm was shot off, and when he came back he became a city traffic engineer, as he could no longer sew. After a long and happy life, he passed away and the family had a chair-type stone created where people could sit and enjoy the view of the cemetery. It is not disrespectful to sit there, but a celebration of this man's life, all discovered because a student saw an unusual stone in the graveyard. His sons are still alive as of this writing, and the student interviewed them for her paper. They were only too glad to speak at length on their father and mother.
Another young student has apparently created a cottage industry out of a gravestone which attracted her. She picked the stones of Isaac Post and his wife. Isaac and Amy Post were big names in mid-nineteenth century Rochester, and knew Susan B Anthony, Frederick Douglass, and other noteworthy people of that time. The key thing here is that Isaac wrote some books dealing with Spiritualism, and in them mentioned some spirits that had come to visit him. Those spirits, as it turned out, were really people who had been murdered . The most interesting was a 13 year-old girl who was killed by her brother-in-law. He was sleeping with her and killed her in a fit of guilt, and then killed himself. (This was circa 1850). The family in which this occurred lived in what is now a suburban town, and continued to live there for decades after this occurrence.
Yet another story - A stone had a listing for a man who had an interesting life. He was well-to-do and traveled a great deal back and forth to Europe. By researching his name in newspapers and in wills, it was found that for the most part he was a devil-may-care playboy sort of person. In fact, one of the newspaper articles turned up was that he was the plaintiff in a defamation of character suit brought by a young woman with whom he had had an affair on the boat trip back from Europe. Once they got back and he left her to come home, she sued him for something akin to alienation of affection, and sullying her good name (after all, this was 100 years ago!). Once the family name and address was known, there appeared a series of clippings in the scrapbook files dealing with the family house - which is now gone and a factory stands in its place.
As it turns out, he won the case and she eventually was sent to prison for bringing a lawsuit with no basis - after all she was a loose woman who "dared to impugn the unsullied reputation" of Mr. So and So. Well, apparently not. He was the brother of another woman who was very litigious herself, and had many lawsuits against the city for taking their land and using it by eminent domain. While these news articles were very entertaining, the point was that they were sparked by a nice gravestone which begged explanation.
The course description reads "symbols and inscriptions express views of life, death, and immortality, which form the subject of [the] class… Students study funeral traditions and ritual, and explore the ways in which the images and words on gravestones help to resolve the loss of a loved one by forging symbolic connections between the living and the dead. As an important part of their research, students are required to select a gravestone or series of stones in Mt. Hope Cemetery and record, photograph, and document all images and inscriptions. Further, they consult the interment records at the Mt. Hope office and search for other relevant sources to illuminate the deaths and lives of their subjects. Students learn the proper methods and procedures for collecting and recording data essential to graveyard preservation, and have the rare opportunity to study and carry-out unprecedented research on one of America's oldest Victorian cemeteries.
The underlying thing about all of this is that a local college goes into a cemetery and does historical and genealogical research in various families. For more information on this particular class, see https://dspace.lib.rochester.edu/handle/1802/46. Various pictures could have been taken, interviews done, and observations made all unbeknownst to you as a family researcher. Another local college has done similar projects for quite a few years, involving a well known local cemetery - {http://www-pub.naz.edu:9000/~tkneela8/) is the link for that class.
What this goes to show you is that perhaps totally unknown to you a local-to-your-ancestors college may have done research on your family, and either posted it on the web or used it for a thesis or similar academic pursuits. You never know until you look.