Microposts are small fragments of social media content and a popular medium for sharing facts, opinions and emotions. Collectively, they comprise a wealth of data that is increasing exponentially, and which therefore presents new challenges for the Information Extraction community, among others. This paper describes the 'Making Sense of Microposts' (#icroposts2015) Workshop's Named Entity rEcognition and Linking (NEEL) Challenge, held as part of the 2015 World Wide Web conference (WWW'15). The challenge task comprised automatic recognition and linking of entities appearing in different event streams of English Microposts on Twitter. Participants were set the task of investigating novel strategies for extracting entities in a tweet stream, typing these based on a set of pre-defined classes, and linking to DBpedia or NIL referents. They were also asked to implement a web service to run their systems, to minimize human involvement in the evaluation and allow measuring of processing times. The challenge attracted a lot of interest: 29 research groups expressed an intent to participate, out of which 21 signed the agreement required to be given a copy of the training and development datasets. Seven teams participated in the final evaluation of the challenge task, out of which six completed all requirements, including submission of an abstract describing their approach. The submissions covered sequential and joint linguistic methods, end-to-end and hybrid end-to-end, and linguistic approaches for approaching the challenge task. We describe the evaluation process and discuss the performance of the different approaches to the #Microposts2015 NEEL Challenge. We also release, with this paper, the #Microposts2015 NEEL Challenge Gold Standard, comprising the set of manually annotated tweets.