Recall that object and class implementations are specific for programming language and compiler. I.e. a Delphi application doesn't know how to work with objects/classes from (for example) Microsoft C++ (and visa versa). This means that hi-level exception raised in DLL could not be properly handled by host application, unless both DLL and host are compiled by the same compiler and exception class uses the virtual destructor.
Also note that mixing OS and language exceptions within same module is confusing/problematic thing.
Therefore, APIs for DLLs usually do not use exceptions as a way to report errors. Instead: functions can use error codes - such as numeric codes, success/failure flags (booleans) and so on. There are de facto standard ways to report errors - provided by operating system (for example: GetLastResult, HRESULT - on Windows). However, 3rd party DLLs may use arbitrary error reporting method.
A simple example:
1. Incorrect (not recommended)
DoSomething function does not catch exceptions, and let exceptions escape to the caller module - which can be written in another programming language. This is a big NO - unless you compile both DLL and caller in the very same version of the compiler.
Note: if you develop DLL that will only be used in executable compiled in exactly the same version of the compiler, and you want to pass exceptions between modules for simplicity - see this article.
2. Correct (recommended)
DoSomething function handles exceptions, thus exceptions are not escaped into the caller. See this article for sample code that may be placed inside except block.
Of course, you also want some way to tell the caller that there was an error when calling your function. See this article for more information. If you are developing your own DLL and API rules for it - see this article.