For some languages, processor specific instructions can be accessed by using extensions made to the language, such as some intrinsic functions for C. For example, Microsoft C has a _popcnt() instrinsic function to utilize the popcnt X86 instruction, which counts the number of 1 bits in a value.
Some super computers add system specific extensions to the Fortran language to take advantage of parallel or vector processing.
Some languages deliberately limit what a programmer can access, such as Python not having assignable pointer variables.
For languages that can be compiled (versus interpreted), usually assembly modules can be linked with high level language modules to get around any limitations of a high level language.