With the rise of institutional and enterprise computing, there was a strong demand for digitization and organization of physical databases. Ranging from business cards in one's rolodex to medical files sitting in the basement archives, these physical artifacts needed a consistent data structure as well as a way to easily communicate with such structure in order to be stored in computer devices: university researchers and enterprise solution companies set out to work.
Early databases featured simple digitized documents, not unlike a messy set of Word documents thrown into a folder, and it was a resource-intensive process to look for a specific piece of content as the system would always have to start from the top. Other proposed solutions included hierarchical / network models, where a set of documents were clustered by role and function, and organized in a tree-like structure to reduce search time. IBM enjoyed great success serving enterprise and government stakeholders with database software based on such models since the 1960s, and still continue to be a major player in this area.
There certainly was room for improvement for then-popular hierarchical models: the user had to make concrete decisions surrounding how data is to be organized, and such decisions were difficult to revert. In the early 70s, IBM's own research division designed a new relational model, which can be described as a network of arbitrary tables: the user could create and remove spreadsheet-like tables at will, and could easily create relationships between different tables by with columns dedicated to hosting such connections.
In addition, the database market struggled with the challenge of having to hire programmers to build tailored yet expensive solutions (to IBM's benefit). There was little consistency, let alone compatibility, between such solutions, and IBM's another research group developed a common language designed to interact with relational databases called SQL (Structured Query Language). Resembling a straightforward yet rigidly structured English command, the user would be able to easily yet clearly add or retrieve database records.
Despite these in-house innovations, IBM was struggling to build prototypes, especially with its massive success with existing customers. Ultimately, IBM was late to the market as the new competitor Oracle distributed the world's first commercially available relational database system, also named Oracle. By the time IBM arrived with its own take on easy-to-use relational database solutions, Oracle has dominated small business and enterprise sectors, and IBM retreated to take control over government solutions.
As the need for small-scale database solutions emerged in personal computing and small business sectors, MySQL AB became an unexpected leader in the open-source market thanks to the eponymous solution. First released in 1995, it is now considered to be the most popular database solution around the world, followed by Microsoft's commercial product SQL Server and other open-source alternatives.
Alongside PHP, MySQL joined the popular LAMP stack, becoming the de facto standard for hosting small business applications and content management systems: many successful startups (ex. early Facebook) bootstrapped using MySQL, and blogging platforms such as WordPress continue to use MySQL due to its availability and ease of use. MySQL also joined the then-revolutionary movement surrounding open-source business model, by being completely free for all parties but charging fees for enterprise support.
Things, however, turned upside down when MySQL AB was sold to Sun Microsystems (of the Java fame), then later to Oracle in 2010. Citing the visible conflict of interest in this eventual sale, a considerable piece of MySQL's market share migrated to other open-source solutions, including PostgreSQL (based on older relational model projects, Ingres and Postgres) and MariaDB, created by disappointed defectors from MySQL AB. Despite the controversy, however, the open-source market for relational database continues to grow as more individuals are looking to experiment with code.