Whatever the type of the exterior walls (masonry, wood-frame, steel-frame...) a layer of insulation all over them (insulation sheathing) is a smart choice for energy savings and thermal comfort.
In wood frame construction, stud insulation is rarely enough and with the exception of some special types of wall assembly design (double 2x4 walls, for instance), you need insulating sheathing, that is, a continuous layer of an insulation product installed on the exterior or the interior of the building structure. That's the best way to minimize heat flow through the framing members and other conductive materials in the walls (thermal bridging).
Insulating sheathing Materials
You can use a number of materials as insulating sheathing, including inexpensive insulation materials such as fiberglass and cellulose. The builder can attach lightweight wood frames to the walls and fill them with sprayed fibrous fiberglass or cellulose: at least six inches of insulation, for a reasonable R-value…Polystyrene foam boards attached to the walls with the help of wood strips, are an easy way of increasing the insulation levels of walls. Other foams: spray polyuretnane and rigid polysocyanuratea.
But the best options, and the ones that are most used in new construction, involve foams (spray polyurethane, rigid polystyrene, rigid polyisocyanuratea) and dense mineral wool. These materials are a lot more effective, and it's risky to use water-sensitive materials such as fiberglass or cellulose...
Retrofit Wall Insulation (Exterior)
In retrofit wall insulation, consider at least 4 inches of foam (or dense mineral wool). It will greatly improve the energy efficiency of your walls.
Interior Wall insulation (Retrofit insulation)
There are cases where adding insulation to the exterior of the walls is not practical; and that's where interior wall insulation enters, with all its obvious disadvantages: reduction of the living space, problems with architraves, moldings, window sills and electrical boxes; or the need to extend jambs around windows and door openings.
Interior vs. Exterior wall insulation in new Buildings
Installing the insulation on the outside provides further protection of the walls and keeps them warm (important to reduce the risk of moisture condensation, in cold climates).
It generally allows a more continuous and more complete covering of the framing and consequently, minimal thermal bridging (unwanted heat loss or gain through the framing).
Putting a continuous layer of insulation material in the middle of the wall can also be a good choice (in double 2x4 wood-frame walls, and some solid and cavity masonry walls) as long as the layer is thick enough and continuous. This choice is very common in super-insulated masonry walls, but also in traditional masonry cavity walls, where the insulation material is installed behind the drainage cavity plane.
Installing the insulation material on the inside of the wall is less common, except in single-leaf masonry walls or in home improvement projects.
Inside wall insulation can be advantageous in buildings with masonry walls, to avoid the negative impact of the masonry during heat waves and very cold weather conditions; in cold climates, interior insulation prevents the walls from absorbing significant amounts of heat (generated by the heating systems) during the cold weather months, allowing a quicker heating; in hot climates, during heat waves, inside wall insulation also prevents masonry walls from absorbing large amounts of solar heat during the day and releasing it during the night, when people are resting.