Traditional life insurance mathematics provides a plentiful toolkit for actuarial calculations. Nevertheless, significant weaknesses appear when relating classical approaches to current needs, which emerge from a continuously moving scenario. First, the equivalence principle reveals its weakness when risky features of the insurance business call for appropriate consideration. Secondly, traditional life insurance mathematics usually focusses on simple products, many of which are no longer in line with current scenarios, either because of financial and biometric aspects of the scenario itself, or because of customer behavior. This presentation starts by focusing on a classical actuarial formula: the expected present value of a deferred life annuity. We then move to the analysis of the (critical) assumptions underpinning that formula, stressing the â€œscopeâ€ of the formula itself which encompasses both the accumulation and the decumulation phase. A survey of products, which can fit individual needs, in the accumulation and the decumulation phase respectively, follows. Special emphasis is placed: (a) on the â€œflexibilityâ€ allowed by some products in terms of available options and possible benefit packaging; (b) on the consequent â€œguaranteesâ€ of financial and biometric nature; (c) on risks borne by the insurance company. Guarantees and inherent risks can be clearly perceived in recent scenarios, especially because of volatility in financial markets and uncertainty in mortality / longevity trends. What lessons can we take from insurersâ€™ strategies and customersâ€™ behavior, in order to update teaching guidelines? First, as regards products, special attention should be placed on â€œcomboâ€ products constructed via packaging benefits and related technical features (natural hedging included). Secondly, equivalence-based calculations should be complemented (if not replaced) by appropriate risk assessments, at least at a portfolio level (as required by current solvency principles), but also at a policy level when significant guarantees are involved (as, for example, in variable annuity products).