This article presents the first systematic review of unsupervised and semi-supervised computational text-based ideal point estimation (CT-IPE) algorithms, methods designed to infer latent political positions from textual data. These algorithms are widely used in political science, communication, computational social science, and computer science to estimate ideological preferences from parliamentary speeches, party manifestos, and social media. Over the past two decades, their development has closely followed broader NLP trends -- beginning with word-frequency models and most recently turning to large language models (LLMs). While this trajectory has greatly expanded the methodological toolkit, it has also produced a fragmented field that lacks systematic comparison and clear guidance for applied use. To address this gap, we identified 25 CT-IPE algorithms through a systematic literature review and conducted a manual content analysis of their modeling assumptions and development contexts. To compare them meaningfully, we introduce a conceptual framework that distinguishes how algorithms generate, capture, and aggregate textual variance. On this basis, we identify four methodological families -- word-frequency, topic modeling, word embedding, and LLM-based approaches -- and critically assess their assumptions, interpretability, scalability, and limitations. Our review offers three contributions. First, it provides a structured synthesis of two decades of algorithm development, clarifying how diverse methods relate to one another. Second, it translates these insights into practical guidance for applied researchers, highlighting trade-offs in transparency, technical requirements, and validation strategies that shape algorithm choice. Third, it emphasizes that differences in estimation outcomes across algorithms are themselves informative, underscoring the need for systematic benchmarking.