Titanium-based alloys are widely used in various industries due to their combination of high mechanical properties and low density. These properties are most effectively used when fabricating aircraft components and medical implants. Shape-memory alloys based on titanium nickelide (nitinol) are promising materials for the fabrication of superelastic medical implants and tools, as well as thermomechanical elements in aerospace technology. The joint application of these materials as elements of hybrid structures or composites is promising for the development of products with a unique set of properties such as high mechanical properties, superelasticity, and damping capacity; increased wear resistance; and thermal shape memory. The basic properties of alloys based on titanium nickelide and the most widely used VT6 titanium alloy (Ti–6Al–4V) are analyzed. It is shown that the combination of functional properties of nitinol and structural properties of titanium alloys in an integrated structure makes it possible to fabricate various products, especially for aerospace and medical industries. To fabricate such structures, various welding (mainly laser and diffusion welding) and soldering methods are currently investigated, and the best prospects are associated with the use of intermediate layers that eliminate the formation of brittle intermetallic phases in permanent joints.