The escalating global demand for polymer products and the consequent disposal challenge necessitate technological and sustainable solutions. Recent advances in the development of materials used in 3D printing equipment are described in this review, with a focus on new biocomposite materials. The investigation delves into biocomposites comprising PLA and its blends with other polymers, reinforced by plant fibers, with a particular focus on research conducted over the last five years. The information related to the raw materials’ physical, chemical, and processing properties necessary for creating biocomposite filament and printed parts were summarized. The best results in terms of tensile and flexural strength were presented and discussed, signposting future research avenues and desirable objectives. The findings elucidate that the inclusion of plant fibers led to a reduction in mechanical strength relative to pure PLA; however, when smaller particle sizes of plant fibers were added in volumes below 10%, it resulted in improved performance. Moreover, physical and/or chemical pretreatment of fibers, along with the isolation of cellulose fibrils, emerged as pivotal strategies for bolstering mechanical strengths. Noteworthy are the promising prospects presented by the incorporation of additives, while the refinement of printing parameters is key to improving the tensile and flexural strength of printed components.