Emojis have become an integral part of modern digital communication. Despite their widespread use, most sentiment analysis methods and models disregard emojis during preprocessing, leading to the loss of vital emotional cues. This paper introduces a curated dataset of sentence pairs, with and without emojis, each annotated across three sentiment categories, to assess the impact of emoji inclusion on sentiment classification. We evaluate emoji-inclusive and emoji-exclusive strategies against our human-determined gold standard, using a range of approaches, including the traditional lexicon-dictionary-based methods, and also artificial intelligence (AI) methods, including pre-trained machine learning (ML) based classifiers, and large language models (LLMs). Results show that retaining emojis significantly enhances the performance of all the LLMs we tested, with models such as Qwen, Deepseek, Bert, and Mistral achieving accuracy improvements of over 25%, over an emoji-exclusive strategy. These findings highlight that emojis carry meaningful semantic and affective signals. We emphasize the limitations of current approaches to emoji handling, where emojis are often ignored or treated as irrelevant noise. Instead, we advocate for more thoughtful methods that recognize emojis as meaningful components of communication and incorporate them as valuable sources of information.