Registers are high-speed storage locations located inside the microprocessor or CPU. They are classified according to their function and include general purpose, segment, index, pointer, and flag registers. General purpose registers include the accumulator, base, counter, and data registers. Segment registers store address information for code, data, stack, and extra segments. Index registers point to source and destination operands. Pointer registers include the instruction pointer, stack pointer, and base pointer. Flag registers hold status information about operations including carry, parity, auxiliary, zero, sign, overflow, trap, direction, and interrupt flags.