Theories for analyzing the stresses and strain in laminated structures and for assessment of their strength are briefly reviewed. In actual practice, a realistic assessment of strength, in many cases, still is a challenge, because in general, there are different failure modes in composite laminates that compete with each other. In addition, in laminate structures, situations with highly localized stresses frequently occur that cannot be assessed by employing a pure stress-based strength-of-materials approach. Sometimes, the stress localizations go along with a high, but finite, stress concentration, and sometimes it goes along with stress singularities, which, within the scope of elasticity theory, means infinitely high stresses. A promising way to predict the effective strength in such cases is the use of hybrid failure criteria within the framework of finite fracture mechanics. This approach is also considered in the present article.