As I recently alluded to, we will be replacing our solver abstraction layer MathProgBase (MPB) with MathOptInterface (MOI). The MOI manual, under construction, lists the key design considerations. At a high level, the main changes are:

Constraints are specified in a very generic way (functioninset). MOI defines standard functions (variablewise identity, affine, quadratic), and sets (nonnegative, cones,
{0,1}
), and solvers choose which combinations of functions and sets to accept as constraints. This structure makes it trivial to add new classes of constraints to MOI, and can even be done without modifying MOI (and JuMP). 
MOI has an entirely new status reporting mechanism to explain what caused the solver to stop and how to interpret the output of the solver. MPBâ€™s status symbols were not very informative in error cases (if the solver stopped because of a time limit, is there a feasible solution available?).

Solvers can return more than one output vector (â€śresultâ€ť).

Almost all information (result vectors, statuses, objective bounds, iteration counts) is now accessed in a unified way with
Attribute
objects. This makes it trivial to ask the solver for any variablewise or constraintwise map like an irreducible inconsistent subset. We have attributes for both primal and dual warmstarts now. 
We refer to all constraints and variables with reference objects, not integer indices. This makes it possible to remove and add variables and constraints if the solver supports doing so.

There is now a general way to modify any aspect of the problem which a solver supports changing. Updated coefficients and bounds go through the same
modifyconstraint!
method.
Overall Iâ€™m very happy with the feel of the new interface. Itâ€™s the outcome of a lot of intense discussions stemming from the developersâ€™ meetup and beyond. Thanks to everyone whoâ€™s participated so far!
As you can imagine, MOI will mean substantial changes for JuMP. JuMP 0.19 will be the first JuMP release to support MOI, and I expect it to be the most breaking release before JuMP 1.0.
What will likely change (in a breaking way) on the JuMP side is:
 How statuses are reported. Weâ€™ll be working with MOIâ€™s much richer status reporting, so you wonâ€™t be checking status symbols from the result of
solve()
anymore.  How constraints are represented internally. This will break many JuMP extensions.
 Duality. MOI aims to define consistent conventions for duals across problem classes. In some cases, the signs may differ from the current MPB conventions.
 Solutions/result vectors.
getvalue
may change (for the better) with the introduction of multiple solutions being returned by the solver. I expect to introduce the concept of the value of a variable in a solution to replace the concept of the value of a variable in a model.  Solverindependent callbacks will not be supported in JuMP/MOI. Instead, weâ€™ll be making it easier to access the solverâ€™s native callbacks directly.
For all of the breakage, here are the things that will become easy to do following the transition to MOI:
 Add new constraint types to JuMP (e.g., indicator constraints, complementarity constraints, piecewise linear constraints, bilinear matrix inequalities)
 Check the feasibility of a solution with respect to the constraints in the model
 Access the irreducible inconsistent subset (IIS) for infeasible problems when provided by a solver, and similar properties
 Modify coefficients and righthand sides in a coherent way
 Delete constraints (and variables)
These may not be be present in JuMP 0.19, but will become much easier to implement for anyone who needs this functionality.
We plan on continuing to support JuMP/MPB on Julia 0.7 to ease the transition.
The MOI transition is a big undertaking, and we have a lot of opportunities for new and existing contributors to help out, especially on polishing the MOI documentation, writing tests, and writing MOI solver wrappers. If you are interested, join the JuMPdev channel and we can figure out an appropriate task based on your interests and experience.
Update: As of December 2018, JuMP 0.19beta is released.