One of the significant challenges in fields of drug discovery and bioinformatics is the prediction of protein’s 3-D structure due to its computational complexity. The vast conformational space and intricate energy functions make it hard to accurately predict protein structures. Two main approaches exist: template-based protein structure prediction uses known protein structures, while template-free protein structure prediction tackles proteins without known structures. Despite recent advancements, precise structures for complex proteins remain elusive for effective drug design. Predicting structures solely from amino acid sequences, known as ab initio prediction, is still unresolved. With an increasing number of proteins lacking known structures, sophisticated artificial intelligence (AI) methods are crucial for further progress. However, AI researchers face hurdles owing to the complex nature of protein structure prediction and limited comprehensive resources. This book chapter provides a comprehensive description of template-free protein structure prediction research, including essential concepts and computational methods. It discusses challenges, offers insights, and suggests directions for future studies to advance computational prediction of protein structure effectively.