The article examines the interaction of resultative and goal phrases with aspect in Polish and English. The first research problem concerns the ability of resultative and goal phrases to aspectually delimit (telicize) an atelic predicate. Data from English shows that resultative and goal phrases systematically make an atelic predicate telic in non-progressive sentences, but they fail to do so in progressive constructions. In Polish, imperfective (atelic) constructions can never be aspectually delimited by such phrases. It is argued that resultative and goal phrases lose their telicizing potential when in the scope of an aspectual functional head Asp specified as [-telic]. This is the case in English progressive and Polish imperfective sentences. The Asp head is able to override the telicity specification established compositionally within VP. The Asp head in Polish is obligatory and the value of its telicity feature ([+telic] for perfective and [-telic] for imperfective) is responsible for the interpretation of the VP selected by Asp as a complement. In English such projection is optional. When it is absent, the telicity of a predicate can be computed from the default aspectual type of the lexical verb combined with other elements inside VP, including resultative and goal phrases. A related problem also addressed in the article concerns the meaning of progressive / imperfective resultative and goal constructions. The problem is presented as part of a larger task of finding a proper analysis for accomplishment predicates combined with a progressive / imperfective operator. The proposed solution is based on the notion of directionality. It is suggested that resultative and goal constructions denote a process of some entity changing in the ‘direction’ of a new state. When the process is understood as having a culmination, the ‘direction’ of the transition indicates a new state actually holding of the entity undergoing transition. When a progressive / imperfective operator is introduced, it can remove the culmination leaving just the directed-transition process. A formalization of this analysis is provided.