Updated Oct 1: tl;dr: Thanks mostly to the persistence of @ExpandingMan, JuMP 0.18.3 was released today supporting Julia 0.6, 0.7, and 1.0. Upgrade away!
If you are using JuMP 0.18 on Julia 0.6, we do recommend upgrading now to Julia 0.7 and JuMP 0.18.3. Use Julia 0.7 to assist with updating existing code. If the code runs without deprecation warnings on Julia 0.7, it should run on Julia 1.0 (with some exceptions). Note however that not all solvers have been updated for Julia 1.0/0.7 yet. (We have 17 solvers under the JuliaOpt organization.) There are known issues with Cbc and Clp. Please give your favorite solver a try and report any issues that arise. Pull requests are even better
As a reminder, JuMP 0.18.x is the last release to support the MathProgBase API. We will continue to support JuMP 0.18.x on Julia 0.6/0.7/1.0, but most developer effort is focused on the next release of JuMP which supports the MathOptInterface (MOI) API. JuMP 0.19 may require Julia 1.0 (this isn’t decided yet). Expect an alpha tag of JuMP 0.19 with accompanying announcement soon.