Industrialization and urbanization are two intertwined processes that have profoundly reshaped family structures across the globe, moving societies from agrarian, largely joint family systems to more diverse and often nuclear family forms. These transformations affect family size, roles, relationships, and functions.

Shift from Joint to Nuclear Family:

1. Economic Necessity: In agrarian societies, the joint family was an economic unit, with multiple generations living and working together on family land. Industrialization, however, shifted work from home/farm to factories and offices, requiring individual mobility. Young adults often migrated to urban centers for employment, leading to the formation of nuclear families (parents and their dependent children) in cities, separate from their extended kin.
2. Space Constraints and Cost of Living: Urban environments, characterized by smaller living spaces and higher costs of living, make it impractical and expensive for large joint families to reside together. This naturally favors smaller, nuclear family units.
3. Individualism and Privacy: Urban life often fosters a greater sense of individualism and a desire for privacy, which is more easily achieved in a nuclear family setting compared to the communal living of a joint family.

Changes in Roles and Relationships:

1. Gender Roles: Industrialization opened up employment opportunities for women outside the home, challenging traditional patriarchal gender roles. Women's economic independence led to greater decision-making power within the family and a demand for more egalitarian relationships. However, it also often resulted in a 'double burden' for women, balancing paid work with domestic responsibilities.
2. Parent-Child Relationships: With children no longer being economic assets (as in farm labor), there's a greater emphasis on their education and emotional well-being. Parents invest more in fewer children, leading to more intense and emotionally focused parent-child relationships. Child labor laws and compulsory education further reinforced this shift.
3. Elderly Care: In joint families, the elderly were traditionally cared for by their children and grandchildren. With the rise of nuclear families and geographical mobility, the responsibility for elderly care often shifts from the family to institutional care, or the elderly may live alone, leading to issues of loneliness and neglect.

Economic and Social Functions of the Family:

1. From Production to Consumption: The family unit largely ceased to be a unit of production (as in farming or cottage industries) and transformed into a unit of consumption, purchasing goods and services from the market.
2. Loss of Traditional Functions: Many functions traditionally performed by the family, such as education, healthcare, and social security, have been increasingly taken over by specialized institutions (schools, hospitals, welfare states).
3. Social Support Systems: While nuclear families offer intimacy, they can also lead to a reduction in the broader social support network provided by extended kin. This can make individuals more vulnerable during crises, though new forms of community and social networks may emerge in urban settings.

Emergence of Diverse Family Forms: Industrialization and urbanization have also contributed to the rise of diverse family forms beyond the traditional nuclear model, including single-parent families, live-in relationships, DINK (Dual Income No Kids) couples, and blended families, reflecting changing social norms and individual choices.

In conclusion, industrialization and urbanization have acted as powerful catalysts, dismantling traditional family structures and functions, and paving the way for more adaptable, smaller, and diverse family units that are better suited to the demands of modern industrial and urban life.