What About Medical Coverage While Abroad ?

I’ve accepted a position that will have me working in several countries over the next eighteen months. My employer handles flights and accommodation, but the personal side of healthcare is apparently left to me. Some assignments could last only a few weeks while others might become much longer. I’m finding it difficult to compare my situation with ordinary business travel because I’ll effectively be living abroad for much of the year. How do people normally approach medical coverage when their work keeps moving them between countries?