Droplet-based microfluidics enables compartmentalization and controlled manipulation of small volumes. Open microfluidics provides increased accessibility, adaptability, and ease of manufacturing compared to closed microfluidic platforms. Here, we begin to build a toolbox for the emerging field of open channel droplet-based microfluidics, combining the ease of use associated with open microfluidic platforms with the benefits of compartmentalization afforded by droplet-based microfluidics. We develop fundamental microfluidic features to control droplets flowing in an immiscible carrier fluid within open microfluidic systems. Our systems use capillary flow to move droplets and carrier fluid through open channels and are easily fabricated through 3D printing, micromilling, or injection molding; further, droplet generation can be accomplished by simply pipetting an aqueous droplet into an empty open channel. We demonstrate on-chip incubation of multiple droplets within an open channel and subsequent transport (using an immiscible carrier phase) for downstream experimentation. We also present a method for tunable droplet splitting in open channels driven by capillary flow. Additional future applications of our toolbox for droplet manipulation in open channels include cell culture and analysis, on-chip microscale reactions, and reagent delivery.