Emerging economy markets : What are the various options to invest?

I believe we have had too much of domination (much more than outperformance) of developed economies over emerging economies. (most of the asian and african, south american countries) where the rewards (demographics, natural resources, potential growth etc) outweigh risks (unstable political developments, corruption , lack of education etc)

What are the different ways to have both direct and indirect exposure to opportunities in these markets ?