What problem do they solve?

If we refer to general code patterns established within a team:

• We use it as an opportunity to discuss benefits and tradeoffs of some patterns around an issue, that are very specific for our applications, business logic and team makeup
• Once we’ve agreed on something as a team, we put it in a code patterns repo with some explanation of why and how we arrived at this agreed pattern.
• It reduces our cognitive load and helps with onboarding. It also helps with introducing a new team to working on the same repos.
• In practice we have done this for patterns in our React, Node and Spring Boot apps.

If we refer to general Design Patterns within the Object Oriented Programming (OOP) paradigm:

• They are good for managing dependencies for your code. It is about arranging what code you have so that it will be easy to change. – An almost word-for-word extract from Practical Object-Oriented Design: An Agile Primer using Ruby (POODR) by Sandi Metz

If we refer to the Gang of Four Design Patterns published in 1995:

• Statically-typed Object Oriented Programming (OOP) languages, and in particular, Java (verbose and old school).
• I tried to re-create these design patterns in Kotlin, and found that quite a few patterns that I selected were solved by the language itself.
• I could be wrong on the first point, as there are resources that do not restrict their materials to using Java as examples.