Historical linguists identify relations due to descent among modern languages, and reconstruct past language forms, using a system known as the Classical Comparative Method (CCM). Like most systems in linguistics, the CCM is rule-based and non-quantitative, loosely akin to formal logic. The frontiers of deep reconstruction, however, will require the interpretation of heterogeneous evidence, much of it diffuse within the lexicon and phonology. Only with properly-formulated likelihood or Bayesian probability methods do we stand a chance of interpreting such diffuse signatures. I will describe recent trends of work in quantitative and computational historical reconstruction, and the enormous range of opportunities that exist, to create a quantitative historical linguistics. I will discuss how far one can get by plugging language data into molecular phylogeny codes, the systematic errors that result, and the need to base systematics on the proper probability model for language change. This will bring us to the role of forward models in maximum-likelihood and Bayesian algorithms, and to the intriguing problem of what meanings are, how words relate to them, and how they may be quantitatively compared across languages and through time.