Biomedical research and discoveries are communicated through scholarly publications and this literature is voluminous, rich in scientific text and growing exponentially by the day. Biomedical journals publish nearly three thousand research articles daily, making literature search a challenging proposition for researchers. Biomolecular events involve genes, proteins, metabolites, and enzymes that provide invaluable insights into biological processes and explain the physiological functional mechanisms. Text mining (TM) or extraction of such events automatically from big data is the only quick and viable solution to gather any useful information. Such events extracted from biological literature have a broad range of applications like database curation, ontology construction, semantic web search and interactive systems. However, automatic extraction has its challenges on account of ambiguity and the diverse nature of natural language and associated linguistic occurrences like speculations, negations etc., which commonly exist in biomedical texts and lead to erroneous elucidation. In the last decade, many strategies have been proposed in this field, using different paradigms like Biomedical natural language processing (BioNLP), machine learning and deep learning. Also, new parallel computing architectures like graphical processing units (GPU) have emerged as possible candidates to accelerate the event extraction pipeline. This paper reviews and provides a summarization of the key approaches in complex biomolecular big data event extraction tasks and recommends a balanced architecture in terms of accuracy, speed, computational cost, and memory usage towards developing a robust GPU-accelerated BioNLP system.