diff --git a/R/reconciliation.R b/R/reconciliation.R
index 71e8ba36..1a025c9f 100644
--- a/R/reconciliation.R
+++ b/R/reconciliation.R
@@ -1,7 +1,16 @@
 #' Forecast reconciliation 
 #' 
-#' This function allows you to specify the method used to reconcile forecasts
-#' in accordance with its key structure.
+#' This function allows you to specify the method for reconciling forecasts for
+#' hierarchical or grouped time series. `aggregate_key()` specifies the 
+#' relationships between the series. After an aggregated `tsibble` is modeled, 
+#' `reconcile()` defines the reconciliation algorithm, which is applied to the 
+#' individual and aggregated forecasts for each forecast horizon.
+#' 
+#' Forecast reconciliation ensures that the relationships between time series 
+#' (e.g. that a national forecast equals the sum of regional forecasts within 
+#' that nation) are maintained in the forecasts. Specific reconciliation methods 
+#' may have different constraints. For example, some only work with aggregations 
+#' that are summations.
 #' 
 #' @param .data A mable.
 #' @param ... Reconciliation methods applied to model columns within `.data`.
@@ -31,8 +40,11 @@ reconcile.mdl_df <- function(.data, ...){
 
 #' Minimum trace forecast reconciliation
 #' 
-#' Reconciles a hierarchy using the minimum trace combination method. The 
-#' response variable of the hierarchy must be aggregated using sums. The 
+#' Reconciles a hierarchy using the minimum trace combination method. This 
+#' approach minimizes the mean squared error of the coherent forecasts across 
+#' the entire collection of time series under the assumption of unbiasedness.
+#' 
+#' The response variable of the hierarchy must be aggregated using sums. The 
 #' forecasted time points must match for all series in the hierarchy (caution:
 #' this is not yet tested for beyond the series length).
 #' 
@@ -43,7 +55,8 @@ reconcile.mdl_df <- function(.data, ...){
 #' package is installed.
 #' 
 #' @seealso 
-#' [`reconcile()`], [`aggregate_key()`]
+#' [`reconcile()`], [`aggregate_key()`],
+#' \url{https://otexts.com/fpp2/reconciliation.html}
 #' 
 #' @references 
 #' Wickramasuriya, S. L., Athanasopoulos, G., & Hyndman, R. J. (2019). Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization. Journal of the American Statistical Association, 1-45. https://doi.org/10.1080/01621459.2018.1448825 
@@ -166,14 +179,19 @@ forecast.lst_mint_mdl <- function(object, key_data,
 #' 
 #' \lifecycle{experimental}
 #' 
-#' Reconciles a hierarchy using the bottom up reconciliation method. The 
-#' response variable of the hierarchy must be aggregated using sums. The 
+#' Reconciles a hierarchy using the bottom up reconciliation method. This
+#' method generates forecasts for all time series at the lowest level, then 
+#' sums them according to the aggregation to create forecasts for each level 
+#' of aggregation.
+#' 
+#' The response variable of the hierarchy must be aggregated using sums. The 
 #' forecasted time points must match for all series in the hierarchy.
 #' 
 #' @param models A column of models in a mable.
 #' 
 #' @seealso 
-#' [`reconcile()`], [`aggregate_key()`]
+#' [`reconcile()`], [`aggregate_key()`],
+#' \url{https://otexts.com/fpp2/bottom-up.html}
 #' @export
 bottom_up <- function(models){
   structure(models, class = c("lst_btmup_mdl", "lst_mdl", "list"))
@@ -213,15 +231,20 @@ forecast.lst_btmup_mdl <- function(object, key_data,
 #' 
 #' \lifecycle{experimental}
 #' 
-#' Reconciles a hierarchy using the top down reconciliation method. The 
-#' response variable of the hierarchy must be aggregated using sums. The 
+#' Reconciles a hierarchy using the top down reconciliation method. This method
+#' generates forecasts for the highest level, then disaggregates these 
+#' forecasts to lower levels using the disaggregation specified in the `method` 
+#' argument.
+#' 
+#' The response variable of the hierarchy must be aggregated using sums. The 
 #' forecasted time points must match for all series in the hierarchy.
 #' 
 #' @param models A column of models in a mable.
 #' @param method The reconciliation method to use.
 #' 
 #' @seealso 
-#' [`reconcile()`], [`aggregate_key()`]
+#' [`reconcile()`], [`aggregate_key()`],
+#' \url{https://otexts.com/fpp2/top-down.html}
 #' 
 #' @export
 top_down <- function(models, method = c("forecast_proportions", "average_proportions", "proportion_averages")){
diff --git a/man/bottom_up.Rd b/man/bottom_up.Rd
index 286da787..be060c39 100644
--- a/man/bottom_up.Rd
+++ b/man/bottom_up.Rd
@@ -13,10 +13,15 @@ bottom_up(models)
 \lifecycle{experimental}
 }
 \details{
-Reconciles a hierarchy using the bottom up reconciliation method. The
-response variable of the hierarchy must be aggregated using sums. The
+Reconciles a hierarchy using the bottom up reconciliation method. This
+method generates forecasts for all time series at the lowest level, then
+sums them according to the aggregation to create forecasts for each level
+of aggregation.
+
+The response variable of the hierarchy must be aggregated using sums. The
 forecasted time points must match for all series in the hierarchy.
 }
 \seealso{
-\code{\link[=reconcile]{reconcile()}}, \code{\link[=aggregate_key]{aggregate_key()}}
+\code{\link[=reconcile]{reconcile()}}, \code{\link[=aggregate_key]{aggregate_key()}},
+\url{https://otexts.com/fpp2/bottom-up.html}
 }
diff --git a/man/min_trace.Rd b/man/min_trace.Rd
index 4106c528..fd72de2d 100644
--- a/man/min_trace.Rd
+++ b/man/min_trace.Rd
@@ -20,8 +20,12 @@ matrix algebra? By default, sparse matrices will be used if the MatrixM
 package is installed.}
 }
 \description{
-Reconciles a hierarchy using the minimum trace combination method. The
-response variable of the hierarchy must be aggregated using sums. The
+Reconciles a hierarchy using the minimum trace combination method. This
+approach minimizes the mean squared error of the coherent forecasts across
+the entire collection of time series under the assumption of unbiasedness.
+}
+\details{
+The response variable of the hierarchy must be aggregated using sums. The
 forecasted time points must match for all series in the hierarchy (caution:
 this is not yet tested for beyond the series length).
 }
@@ -29,5 +33,6 @@ this is not yet tested for beyond the series length).
 Wickramasuriya, S. L., Athanasopoulos, G., & Hyndman, R. J. (2019). Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization. Journal of the American Statistical Association, 1-45. https://doi.org/10.1080/01621459.2018.1448825
 }
 \seealso{
-\code{\link[=reconcile]{reconcile()}}, \code{\link[=aggregate_key]{aggregate_key()}}
+\code{\link[=reconcile]{reconcile()}}, \code{\link[=aggregate_key]{aggregate_key()}},
+\url{https://otexts.com/fpp2/reconciliation.html}
 }
diff --git a/man/reconcile.Rd b/man/reconcile.Rd
index 9abbb5d4..673bdcc3 100644
--- a/man/reconcile.Rd
+++ b/man/reconcile.Rd
@@ -15,8 +15,18 @@ reconcile(.data, ...)
 \item{...}{Reconciliation methods applied to model columns within \code{.data}.}
 }
 \description{
-This function allows you to specify the method used to reconcile forecasts
-in accordance with its key structure.
+This function allows you to specify the method for reconciling forecasts for
+hierarchical or grouped time series. \code{aggregate_key()} specifies the
+relationships between the series. After an aggregated \code{tsibble} is modeled,
+\code{reconcile()} defines the reconciliation algorithm, which is applied to the
+individual and aggregated forecasts for each forecast horizon.
+}
+\details{
+Forecast reconciliation ensures that the relationships between time series
+(e.g. that a national forecast equals the sum of regional forecasts within
+that nation) are maintained in the forecasts. Specific reconciliation methods
+may have different constraints. For example, some only work with aggregations
+that are summations.
 }
 \examples{
 if (requireNamespace("fable", quietly = TRUE)) {
diff --git a/man/top_down.Rd b/man/top_down.Rd
index 4c589dd6..2683fcac 100644
--- a/man/top_down.Rd
+++ b/man/top_down.Rd
@@ -18,10 +18,15 @@ top_down(
 \lifecycle{experimental}
 }
 \details{
-Reconciles a hierarchy using the top down reconciliation method. The
-response variable of the hierarchy must be aggregated using sums. The
+Reconciles a hierarchy using the top down reconciliation method. This method
+generates forecasts for the highest level, then disaggregates these
+forecasts to lower levels using the disaggregation specified in the \code{method}
+argument.
+
+The response variable of the hierarchy must be aggregated using sums. The
 forecasted time points must match for all series in the hierarchy.
 }
 \seealso{
-\code{\link[=reconcile]{reconcile()}}, \code{\link[=aggregate_key]{aggregate_key()}}
+\code{\link[=reconcile]{reconcile()}}, \code{\link[=aggregate_key]{aggregate_key()}},
+\url{https://otexts.com/fpp2/top-down.html}
 }