The blockchain technology has come out as the backbone of Distributed Ledger Technology (DLT) since it can enable the means of creating trust to distributed systems whereby no trust is inherently created in such systems. This role involves the consensus mechanism; the mechanism ascertains consistency, penalty of ordering, and the preservation of transaction histories in all nodes that are involved. In this work, a detailed comparative study of blockchain consensus mechanisms is provided based on the Security-Decentralization-Scalability (S-D-C) Trilemma paradigm. The framework argues that blockchain systems cannot simultaneously achieve high levels of the three properties. Formal mathematical descriptions of each of the three elements of the trilemma are given and the extent to which different consensus paradigms, i.e., Proof-of-Work (PoW), Proof-of-Stake (PoS) and Byzantine Fault Tolerance (BFT) forms address the necessary trade-offs is assessed. Modern-day reforms of architecture like sharding, Directed Acyclic Graphs (DAGs) and layered architecture are also analyzed. According to empirical measurements of performance, there are dramatic differences: the classic PoW can only serve about seven transactions per second (tx/s) with finality lag of 60 min, in contrast to optimized BFT systems, which can handle between 3,500 and 7,380 transactions and Layer 2 solutions exceed 10,000. The gaps in research are identified, which are central to this regard: the lack of strong mathematical models of sharding security and of dynamic adaptation mechanisms. This paper provides a conceptual roadmap in assessing consensus mechanisms and sets the stage for future studies to overcome the obstacles of scalability of blockchain technology.