Did The Romans Have Funerals?

The Romans did indeed have funerals and a funeral was reputed to be the most important indicator of social standing, so the bigger and better the funeral, the more important the person.
The Romans had undertakers who prepared the body for death.  However, they would also have professional mourners who would arrive to display their 'grief'.  Whilst the body was being taken to the cemetery the professional mourners and musicians would lead the way, followed by close friends and family.    
Usually a speech was given, honouring the dead person and imploring the mercy of the gods.  The body was then usually placed on a funeral pyre and the pyre was lit.  
After the funeral was over, a funeral feast was held by family and friends.  Meanwhile, the undertakers would take the charred bones of the deceased and put them in an urn.  This would then be placed in a glass urn and set in a tomb or burial chamber (depending on status).