Deep learning has recently experienced explosive growth in use, largely due to advances in neural networks and the availability of large corpora of domain data. Project management activities generate and handle large volumes of data. Software engineering closely relates to project management, so software engineering projects must be prone to the use of neural networks. We seek to obtain an accurate vision of how neural networks are being used in software engineering projects through a systematic mapping study. We confirm that neural networks have already made their way into these projects; however, we show that their current uses are limited to certain repetitive and legacy tasks. Given uncovered ample room for expansion, we point out a few directions the industry and academy can lean toward to in the next years for taking better advantage of neural networks in software engineering projects and immediately advancing the field. We investigate if, how, and to what extent have neural networks been employed to the advancement of software engineering projects. As such, a systematic mapping study was conducted, which led to the conclusion that even though these algorithms have indeed been employed on several software engineering tasks, this employment so far has been shy, mostly relying on legacy types of neural networks. More modern variants, namely, deep learning algorithms, are slowly gaining momentum and should be the trend going forward.