This varies by mission.
The missions were secularized and most of the land and buildings sold starting in 1833-34. Some neophytes continued to live on or near the missions for a decade or more, and some churches continue to operate (Santa Barbara and Santa Ines, for example, have pretty much been in continuous operation since they were founded). Other missions crumbled into dust (Soledad, for example). A portion of the original mission lands were restored to the Catholic church after California became part of the United States (President Lincoln returned some mission, like San Juan Capistrano, for example). Efforts were made to restore many of these historic buildings over the next century. The restoration effort gathered steam in the early years of 20th century.
Today some of these restored missions function as parish churches (San Fernando Rey, for example). At other missions (San Francisco de Asis, for example) the original mission church is used as a chapel for the larger parish church next door. A seminary (to train future priests) was located at Mission Santa Barbara, which also has rooms housing the official mission archives. A few missions are still occupied by Franciscans (San Luis Rey, for example). Other mission ultimately fell into private hands and were later sold or given to the state, and are now the nucleus of a state park (La Purisima, for example). The land has changed around all the missions except San Antonio de Padua which still looks much as it did in the mission era.
So in summary a lot has changed in the role the missions play in society and the activities that take place there. However the essence of the mission system is still intact. The missions are [for the most part] in the same location, contain a mission church and some of the original grounds, and they display precious historic objects that are authentic – all of which help us envision how the missions were over two hundred years ago.