The options:

Drop rows with missing. Simplest. Use when: dropping doesn't bias your analysis and you have plenty of data. Fails when: missing isn't random (dropping skews your sample).
Drop the column. If too many rows are missing (say, >40%), the column may not be usable at all.
Impute with mean / median / mode. Simple, common. Mean fine for symmetric distributions; median better for skewed. Downside: reduces variance, biases correlations toward zero.
Impute with a constant (0 / -1 / 'Unknown'). Fine for categorical features where 'missing' is itself meaningful. Dangerous for numeric if the constant carries meaning (don't impute 0 into revenue).
Forward-fill / backward-fill (for time-series or ordered data). 'Carry the last observed value forward' is often appropriate for metrics with inherent continuity.
Model-based imputation. Use other columns to predict the missing value (K-NN, regression, MICE — multiple imputation by chained equations). More accurate but more complex.
Add 'missing' as a feature. For ML: include a boolean 'was_missing' flag alongside the imputed value. The fact of missingness is often itself predictive.
Use a model that handles missing. XGBoost, LightGBM handle missing natively. Can avoid imputation entirely.

The key question: why is it missing?

Missing Completely at Random (MCAR). Pure random drop. Any imputation is fine.
Missing at Random (MAR). Missingness depends on other observed columns. Imputation using those columns works.
Missing Not at Random (MNAR). Missingness depends on the missing value itself (e.g., high-income respondents skip income questions). Imputation can't fix this; you need to model the missingness process or acknowledge the bias.

Diagnose by:

Comparing distributions of other columns for rows with/without missing values.
Knowing the data collection process (why might this value be missing?).

Practical recipe for most datasets:

Profile: how much is missing, and where?
If <5% in a column and distributed randomly: mean/median impute.
If 5-40% in a column: consider model-based imputation OR add 'was_missing' as a feature.
If >40%: reconsider including the column at all.
Always document what you did. 'I imputed with mean' is better than silently doing it.

Reporting to stakeholders:

"The income column is 15% missing. Imputation by overall mean would bias analysis — missingness correlates with high-income respondents (they skip the question more). I'll impute using a regression model with other demographic fields, add a 'was_missing' flag, and report sensitivity to imputation choice."

What senior candidates add:

Reference the MCAR/MAR/MNAR framework explicitly.
Discuss multiple imputation (MICE) as the rigorous approach for MAR situations.
Note that in A/B testing, missing outcomes require careful thought — you can't impute them away without biasing the effect estimate.

How do you handle missing values?

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