To separate the clauses of a compound sentence when the conjunction is omitted

Between the clauses of a compound sentence that are joined by one of the conjunctive adverbs: accordingly, also, besides, consequently, further, hence, furthermore, however, moreover, nevertheless, otherwise, still, then, thus, yet, or therefore

To separate units in a series when they are long and complicated or internally punctuated

Between clauses of a compound sentence that are connected by a conjunction when those clauses are somewhat long, or when a more decided pause is desirable